diff --git a/src/rules/no-duplicate-imports.js b/src/rules/no-duplicate-imports.js
index 0580156..d16a247 100644
--- a/src/rules/no-duplicate-imports.js
+++ b/src/rules/no-duplicate-imports.js
@@ -52,9 +52,19 @@ export default {
 						data: { url },
 						fix(fixer) {
 							const [start, end] = sourceCode.getRange(node);
+							const text = sourceCode.text;
 							// Remove the node, and also remove a following newline if present
-							const removeEnd =
-								sourceCode.text[end] === "\n" ? end + 1 : end;
+							let removeEnd = end;
+							if (text[removeEnd] === "\r") {
+								removeEnd +=
+									text[removeEnd + 1] === "\n" ? 2 : 1;
+							} else if (
+								text[removeEnd] === "\n" ||
+								text[removeEnd] === "\f"
+							) {
+								removeEnd += 1;
+							}
+
 							return fixer.removeRange([start, removeEnd]);
 						},
 					});
diff --git a/src/rules/no-important.js b/src/rules/no-important.js
index a9a3b56..07e0435 100644
--- a/src/rules/no-important.js
+++ b/src/rules/no-important.js
@@ -55,7 +55,7 @@ export default {
 					const textWithoutComments = declarationText.replace(
 						commentPattern,
 						/* eslint-disable-next-line require-unicode-regexp -- we want to replace each code unit with a space */
-						match => match.replace(/[^\n]/g, " "),
+						match => match.replace(/[^\r\n\f]/g, " "),
 					);
 					const importantMatch =
 						importantPattern.exec(textWithoutComments);
diff --git a/tests/rules/no-duplicate-imports.test.js b/tests/rules/no-duplicate-imports.test.js
index f670bb8..6b2bb3c 100644
--- a/tests/rules/no-duplicate-imports.test.js
+++ b/tests/rules/no-duplicate-imports.test.js
@@ -238,5 +238,47 @@ ruleTester.run("no-duplicate-imports", rule, {
 				},
 			],
 		},
+		{
+			code: "@import url('a.css');\r\n@import url('a.css');\r\n@import url('b.css');",
+			output: "@import url('a.css');\r\n@import url('b.css');",
+			errors: [
+				{
+					messageId: "duplicateImport",
+					data: { url: "a.css" },
+					line: 2,
+					column: 1,
+					endLine: 2,
+					endColumn: 22,
+				},
+			],
+		},
+		{
+			code: "@import url('a.css');\r@import url('a.css');\r@import url('b.css');",
+			output: "@import url('a.css');\r@import url('b.css');",
+			errors: [
+				{
+					messageId: "duplicateImport",
+					data: { url: "a.css" },
+					line: 2,
+					column: 1,
+					endLine: 2,
+					endColumn: 22,
+				},
+			],
+		},
+		{
+			code: "@import url('a.css');\f@import url('a.css');\f@import url('b.css');",
+			output: "@import url('a.css');\f@import url('b.css');",
+			errors: [
+				{
+					messageId: "duplicateImport",
+					data: { url: "a.css" },
+					line: 2,
+					column: 1,
+					endLine: 2,
+					endColumn: 22,
+				},
+			],
+		},
 	],
 });
diff --git a/tests/rules/no-important.test.js b/tests/rules/no-important.test.js
index 86fe10d..be6ee62 100644
--- a/tests/rules/no-important.test.js
+++ b/tests/rules/no-important.test.js
@@ -200,6 +200,60 @@ ruleTester.run("no-important", rule, {
 				},
 			],
 		},
+		{
+			code: "a { color: red\r\n!important; }",
+			errors: [
+				{
+					messageId: "unexpectedImportant",
+					line: 2,
+					column: 1,
+					endLine: 2,
+					endColumn: 11,
+					suggestions: [
+						{
+							messageId: "removeImportant",
+							output: "a { color: red; }",
+						},
+					],
+				},
+			],
+		},
+		{
+			code: "a { color: red\r!important; }",
+			errors: [
+				{
+					messageId: "unexpectedImportant",
+					line: 2,
+					column: 1,
+					endLine: 2,
+					endColumn: 11,
+					suggestions: [
+						{
+							messageId: "removeImportant",
+							output: "a { color: red; }",
+						},
+					],
+				},
+			],
+		},
+		{
+			code: "a { color: red\f!important; }",
+			errors: [
+				{
+					messageId: "unexpectedImportant",
+					line: 2,
+					column: 1,
+					endLine: 2,
+					endColumn: 11,
+					suggestions: [
+						{
+							messageId: "removeImportant",
+							output: "a { color: red; }",
+						},
+					],
+				},
+			],
+		},
 		{
 			code: dedent`
 				a {