diff --git a/.README/rules/require-template.md b/.README/rules/require-template.md
index f90cad4c..a76b30ef 100644
--- a/.README/rules/require-template.md
+++ b/.README/rules/require-template.md
@@ -20,8 +20,8 @@ or
 
 Note that in the latter TypeScript-flavor JavaScript example, there is no way
 for us to firmly distinguish between `D` and `V` as type parameters or as some
-other identifiers, so we use an algorithm that any single capital letters
-are assumed to be templates.
+other identifiers, so we use an algorithm that assumes that any single capital
+letters are templates.
 
 ## Options
 
diff --git a/docs/rules/require-template.md b/docs/rules/require-template.md
index 581270a5..df907df9 100644
--- a/docs/rules/require-template.md
+++ b/docs/rules/require-template.md
@@ -22,8 +22,8 @@ or
 
 Note that in the latter TypeScript-flavor JavaScript example, there is no way
 for us to firmly distinguish between `D` and `V` as type parameters or as some
-other identifiers, so we use an algorithm that any single capital letters
-are assumed to be templates.
+other identifiers, so we use an algorithm that assumes that any single capital
+letters are templates.
 
 <a name="user-content-require-template-options"></a>
 <a name="require-template-options"></a>
@@ -199,6 +199,18 @@ export default class <NumType> {
   add: (x: NumType, y: NumType) => NumType;
 }
 // Message: Missing @template NumType
+
+/**
+ * @callback
+ * @param {[D, V | undefined]} someParam
+ */
+// Message: Missing @template D
+
+/**
+ * @callback
+ * @returns {[D, V | undefined]}
+ */
+// Message: Missing @template D
 ````
 
 
@@ -323,5 +335,24 @@ export default class <NumType> {
   zeroValue: NumType;
   add: (x: NumType, y: NumType) => NumType;
 }
+
+/**
+ * @callback
+ * @template D
+ * @template V
+ * @param {[D, V | undefined]} someParam
+ */
+
+/**
+ * @callback
+ * @template D
+ * @template V
+ * @returns {[D, V | undefined]}
+ */
+
+/**
+ * @callback
+ * @returns {[Something | undefined]}
+ */
 ````
 
diff --git a/src/rules/requireTemplate.js b/src/rules/requireTemplate.js
index 8cdf8a59..7e01c247 100644
--- a/src/rules/requireTemplate.js
+++ b/src/rules/requireTemplate.js
@@ -89,12 +89,6 @@ export default iterateJsdoc(({
     }
   };
 
-  const typedefTags = utils.getTags('typedef');
-  if (!typedefTags.length || typedefTags.length >= 2) {
-    handleTypes();
-    return;
-  }
-
   const usedNameToTag = new Map();
 
   /**
@@ -124,23 +118,45 @@ export default iterateJsdoc(({
     });
   };
 
-  const potentialTypedef = typedefTags[0];
-  checkForUsedTypes(potentialTypedef);
+  /**
+   * @param {string[]} tagNames
+   */
+  const checkTagsAndTemplates = (tagNames) => {
+    for (const tagName of tagNames) {
+      const preferredTagName = /** @type {string} */ (utils.getPreferredTagName({
+        tagName,
+      }));
+      const matchingTags = utils.getTags(preferredTagName);
+      for (const matchingTag of matchingTags) {
+        checkForUsedTypes(matchingTag);
+      }
+    }
+
+    // Could check against whitelist/blacklist
+    for (const usedName of usedNames) {
+      if (!templateNames.includes(usedName)) {
+        report(`Missing @template ${usedName}`, null, usedNameToTag.get(usedName));
+      }
+    }
+  };
 
-  const tagName = /** @type {string} */ (utils.getPreferredTagName({
-    tagName: 'property',
-  }));
-  const propertyTags = utils.getTags(tagName);
-  for (const propertyTag of propertyTags) {
-    checkForUsedTypes(propertyTag);
+  const callbackTags = utils.getTags('callback');
+  const functionTags = utils.getTags('function');
+  if (callbackTags.length || functionTags.length) {
+    checkTagsAndTemplates(['param', 'returns']);
+    return;
   }
 
-  // Could check against whitelist/blacklist
-  for (const usedName of usedNames) {
-    if (!templateNames.includes(usedName)) {
-      report(`Missing @template ${usedName}`, null, usedNameToTag.get(usedName));
-    }
+  const typedefTags = utils.getTags('typedef');
+  if (!typedefTags.length || typedefTags.length >= 2) {
+    handleTypes();
+    return;
   }
+
+  const potentialTypedef = typedefTags[0];
+  checkForUsedTypes(potentialTypedef);
+
+  checkTagsAndTemplates(['property']);
 }, {
   iterateAllJsdocs: true,
   meta: {
diff --git a/test/rules/assertions/requireTemplate.js b/test/rules/assertions/requireTemplate.js
index c2f713a2..ccfb6a36 100644
--- a/test/rules/assertions/requireTemplate.js
+++ b/test/rules/assertions/requireTemplate.js
@@ -365,6 +365,42 @@ export default {
         parser: typescriptEslintParser
       },
     },
+    {
+      code: `
+        /**
+         * @callback
+         * @param {[D, V | undefined]} someParam
+         */
+      `,
+      errors: [
+        {
+          line: 4,
+          message: 'Missing @template D',
+        },
+        {
+          line: 4,
+          message: 'Missing @template V',
+        },
+      ],
+    },
+    {
+      code: `
+        /**
+         * @callback
+         * @returns {[D, V | undefined]}
+         */
+      `,
+      errors: [
+        {
+          line: 4,
+          message: 'Missing @template D',
+        },
+        {
+          line: 4,
+          message: 'Missing @template V',
+        },
+      ],
+    },
   ],
   valid: [
     {
@@ -568,5 +604,33 @@ export default {
         parser: typescriptEslintParser
       },
     },
+    {
+      code: `
+        /**
+         * @callback
+         * @template D
+         * @template V
+         * @param {[D, V | undefined]} someParam
+         */
+      `,
+    },
+    {
+      code: `
+        /**
+         * @callback
+         * @template D
+         * @template V
+         * @returns {[D, V | undefined]}
+         */
+      `,
+    },
+    {
+      code: `
+        /**
+         * @callback
+         * @returns {[Something | undefined]}
+         */
+      `,
+    },
   ],
 };