diff --git a/lib/md037.js b/lib/md037.js
index d4112b8c..14390837 100644
--- a/lib/md037.js
+++ b/lib/md037.js
@@ -2,7 +2,7 @@
 
 "use strict";
 
-const { addErrorContext, forEachLine } = require("../helpers");
+const { addErrorContext, forEachLine, isBlankLine } = require("../helpers");
 const { lineMetadata } = require("./cache");
 
 const emphasisRe = /(^|[^\\])(?:(\*\*?\*?)|(__?_?))/g;
@@ -15,21 +15,72 @@ module.exports = {
   "description": "Spaces inside emphasis markers",
   "tags": [ "whitespace", "emphasis" ],
   "function": function MD037(params, onError) {
+    // eslint-disable-next-line init-declarations
+    let effectiveEmphasisLength, emphasisIndex, emphasisLength, pendingError;
+    // eslint-disable-next-line jsdoc/require-jsdoc
+    function resetRunTracking() {
+      emphasisIndex = -1;
+      emphasisLength = 0;
+      effectiveEmphasisLength = 0;
+      pendingError = null;
+    }
+    // eslint-disable-next-line jsdoc/require-jsdoc
+    function handleRunEnd(line, lineIndex, contextLength, match, matchIndex) {
+      // Close current run
+      let content = line.substring(emphasisIndex, matchIndex);
+      if (!emphasisLength) {
+        content = content.trimStart();
+      }
+      if (!match) {
+        content = content.trimEnd();
+      }
+      const leftSpace = leftSpaceRe.test(content);
+      const rightSpace = rightSpaceRe.test(content);
+      if (leftSpace || rightSpace) {
+        // Report the violation
+        const contextStart = emphasisIndex - emphasisLength;
+        const contextEnd = matchIndex + contextLength;
+        const context = line.substring(contextStart, contextEnd);
+        const column = contextStart + 1;
+        const length = contextEnd - contextStart;
+        const leftMarker = line.substring(contextStart, emphasisIndex);
+        const rightMarker = match ? (match[2] || match[3]) : "";
+        const fixedText = `${leftMarker}${content.trim()}${rightMarker}`;
+        return [
+          onError,
+          lineIndex + 1,
+          context,
+          leftSpace,
+          rightSpace,
+          [ column, length ],
+          {
+            "editColumn": column,
+            "deleteCount": length,
+            "insertText": fixedText
+          }
+        ];
+      }
+      return null;
+    }
+    // Initialize
+    resetRunTracking();
     forEachLine(
       lineMetadata(),
-      (line, lineIndex, inCode, onFence, inTable, inItem, inBreak) => {
-        if (inCode || inBreak) {
+      (line, lineIndex, inCode, onFence, inTable, inItem, onBreak) => {
+        const onItemStart = (inItem === 1);
+        if (inCode || inTable || onBreak || onItemStart || isBlankLine(line)) {
+          // Emphasis resets when leaving a block
+          resetRunTracking();
+        }
+        if (inCode || onBreak) {
           // Emphasis has no meaning here
           return;
         }
-        if (inItem === 1) {
+        if (onItemStart) {
           // Trim overlapping '*' list item marker
           line = line.replace(asteriskListItemMarkerRe, "$1 $2");
         }
         let match = null;
-        let emphasisIndex = -1;
-        let emphasisLength = 0;
-        let effectiveEmphasisLength = 0;
         // Match all emphasis-looking runs in the line...
         while ((match = emphasisRe.exec(line))) {
           const matchIndex = match.index + match[1].length;
@@ -40,38 +91,18 @@ module.exports = {
             emphasisLength = matchLength;
             effectiveEmphasisLength = matchLength;
           } else if (matchLength === effectiveEmphasisLength) {
-            // Close current run
-            const content = line.substring(emphasisIndex, matchIndex);
-            const leftSpace = leftSpaceRe.test(content);
-            const rightSpace = rightSpaceRe.test(content);
-            if (leftSpace || rightSpace) {
-              // Report the violation
-              const contextStart = emphasisIndex - emphasisLength;
-              const contextEnd = matchIndex + effectiveEmphasisLength;
-              const context = line.substring(contextStart, contextEnd);
-              const column = contextStart + 1;
-              const length = contextEnd - contextStart;
-              const leftMarker = line.substring(contextStart, emphasisIndex);
-              const rightMarker = match[2] || match[3];
-              const fixedText = `${leftMarker}${content.trim()}${rightMarker}`;
-              addErrorContext(
-                onError,
-                lineIndex + 1,
-                context,
-                leftSpace,
-                rightSpace,
-                [ column, length ],
-                {
-                  "editColumn": column,
-                  "deleteCount": length,
-                  "insertText": fixedText
-                }
-              );
+            // Ending an existing run, report any pending error
+            if (pendingError) {
+              addErrorContext(...pendingError);
+              pendingError = null;
+            }
+            const error = handleRunEnd(
+              line, lineIndex, effectiveEmphasisLength, match, matchIndex);
+            if (error) {
+              addErrorContext(...error);
             }
             // Reset
-            emphasisIndex = -1;
-            emphasisLength = 0;
-            effectiveEmphasisLength = 0;
+            resetRunTracking();
           } else if (matchLength === 3) {
             // Swap internal run length (1->2 or 2->1)
             effectiveEmphasisLength = matchLength - effectiveEmphasisLength;
@@ -83,6 +114,13 @@ module.exports = {
             effectiveEmphasisLength += matchLength;
           }
         }
+        if (emphasisIndex !== -1) {
+          pendingError = pendingError ||
+            handleRunEnd(line, lineIndex, 0, null, line.length);
+          // Adjust for pending run on new line
+          emphasisIndex = 0;
+          emphasisLength = 0;
+        }
       }
     );
   }
diff --git a/test/detailed-results-MD031-MD040.md b/test/detailed-results-MD031-MD040.md
index 47f11d5c..6dc52a18 100644
--- a/test/detailed-results-MD031-MD040.md
+++ b/test/detailed-results-MD031-MD040.md
@@ -58,3 +58,6 @@ span```` text
 text.
 
 Text [ space](link) text [space ](link) text [ space ](link) text.
+
+Space * inside
+multi-line * emphasis.
diff --git a/test/detailed-results-MD031-MD040.md.fixed b/test/detailed-results-MD031-MD040.md.fixed
index 70e70654..452d77b9 100644
--- a/test/detailed-results-MD031-MD040.md.fixed
+++ b/test/detailed-results-MD031-MD040.md.fixed
@@ -60,3 +60,6 @@ span```` text
 text.
 
 Text [space](link) text [space](link) text [space](link) text.
+
+Space *inside
+multi-line* emphasis.
diff --git a/test/detailed-results-MD031-MD040.results.json b/test/detailed-results-MD031-MD040.results.json
index 059d825a..307040f3 100644
--- a/test/detailed-results-MD031-MD040.results.json
+++ b/test/detailed-results-MD031-MD040.results.json
@@ -116,6 +116,24 @@
         "errorContext": "__ some __",
         "errorRange": [ 19, 10 ]
     },
+    {
+        "lineNumber": 62,
+        "ruleNames": [ "MD037", "no-space-in-emphasis" ],
+        "ruleDescription": "Spaces inside emphasis markers",
+        "ruleInformation": "https://github.com/DavidAnson/markdownlint/blob/v0.0.0/doc/Rules.md#md037",
+        "errorDetail": null,
+        "errorContext": "* inside",
+        "errorRange": [ 7, 8 ]
+    },
+    {
+        "lineNumber": 63,
+        "ruleNames": [ "MD037", "no-space-in-emphasis" ],
+        "ruleDescription": "Spaces inside emphasis markers",
+        "ruleInformation": "https://github.com/DavidAnson/markdownlint/blob/v0.0.0/doc/Rules.md#md037",
+        "errorDetail": null,
+        "errorContext": "multi-line *",
+        "errorRange": [ 1, 12 ]
+    },
     {
         "lineNumber": 17,
         "ruleNames": [ "MD038", "no-space-in-code" ],
diff --git a/test/spaces-inside-emphasis-markers-multiple-lines.md b/test/spaces-inside-emphasis-markers-multiple-lines.md
new file mode 100644
index 00000000..76ad38ec
--- /dev/null
+++ b/test/spaces-inside-emphasis-markers-multiple-lines.md
@@ -0,0 +1,75 @@
+# Space Inside Emphasis Markers, Multiple Lines
+
+Text *emphasis
+emphasis* text
+
+Text *emphasis* *emphasis
+emphasis* *emphasis* text
+
+Text *emphasis* text *emphasis
+emphasis* text *emphasis* text
+
+Text *emphasis* *emphasis
+emphasis* *emphasis* *emphasis
+emphasis* text *emphasis
+emphasis* text *emphasis* text
+
+Text text
+text *emphasis
+emphasis emphasis
+emphasis* text
+text text
+
+Text * asterisk
+
+Text * asterisk
+
+* Item *emphasis* item
+* Item *emphasis* item
+* Item *emphasis
+  emphasis* item
+* Item *emphasis* item
+
+* Item * asterisk
+* Item * asterisk
+
+Text * emphasis {MD037}
+emphasis* text
+
+Text *emphasis
+emphasis * text {MD037}
+
+Text * emphasis {MD037}
+emphasis * text {MD037}
+
+Text *emphasis * *emphasis {MD037}
+emphasis* * emphasis* text {MD037}
+
+Text *emphasis* * emphasis {MD037}
+emphasis * *emphasis* text {MD037}
+
+Text * emphasis * * emphasis {MD037}
+emphasis * * emphasis * text {MD037}
+
+Text text
+text * emphasis {MD037}
+emphasis emphasis
+emphasis * text {MD037}
+text text
+
+* Item *emphasis* item
+* Item * emphasis {MD037}
+  emphasis* item
+* Item *emphasis
+  emphasis * item {MD037}
+* Item * emphasis {MD037}
+  emphasis * item {MD037}
+* Item *emphasis* item
+* Item item item
+  item * emphasis * item {MD037}
+
+Text _ emphasis {MD037}
+emphasis _ text {MD037}
+
+Text ** bold {MD037}
+bold ** text {MD037}