diff --git a/pre_commit_hooks/requirements_txt_fixer.py b/pre_commit_hooks/requirements_txt_fixer.py
index dc41815..6190692 100644
--- a/pre_commit_hooks/requirements_txt_fixer.py
+++ b/pre_commit_hooks/requirements_txt_fixer.py
@@ -34,6 +34,18 @@ class Requirement:
         else:
             return self.name < requirement.name
 
+    def is_complete(self) -> bool:
+        return (
+            self.value is not None and
+            not self.value.rstrip(b'\r\n').endswith(b'\\')
+        )
+
+    def append_value(self, value: bytes) -> None:
+        if self.value is not None:
+            self.value += value
+        else:
+            self.value = value
+
 
 def fix_requirements(f: IO[bytes]) -> int:
     requirements: List[Requirement] = []
@@ -55,7 +67,7 @@ def fix_requirements(f: IO[bytes]) -> int:
         # If the most recent requirement object has a value, then it's
         # time to start building the next requirement object.
 
-        if not len(requirements) or requirements[-1].value is not None:
+        if not len(requirements) or requirements[-1].is_complete():
             requirements.append(Requirement())
 
         requirement = requirements[-1]
@@ -73,7 +85,7 @@ def fix_requirements(f: IO[bytes]) -> int:
         elif line.startswith(b'#') or line.strip() == b'':
             requirement.comments.append(line)
         else:
-            requirement.value = line
+            requirement.append_value(line)
 
     # if a file ends in a comment, preserve it at the end
     if requirements[-1].value is None:

diff --git a/tests/requirements_txt_fixer_test.py b/tests/requirements_txt_fixer_test.py
index 7b9b07d..17a9a41 100644
--- a/tests/requirements_txt_fixer_test.py
+++ b/tests/requirements_txt_fixer_test.py
@@ -50,6 +50,24 @@ from pre_commit_hooks.requirements_txt_fixer import Requirement
             FAIL,
             b'Django\nijk\ngit+ssh://git_url@tag#egg=ocflib\n',
         ),
+        (
+            b'b==1.0.0\n'
+            b'c=2.0.0 \\\n'
+            b' --hash=sha256:abcd\n'
+            b'a=3.0.0 \\\n'
+            b'  --hash=sha256:a1b1c1d1',
+            FAIL,
+            b'a=3.0.0 \\\n'
+            b'  --hash=sha256:a1b1c1d1\n'
+            b'b==1.0.0\n'
+            b'c=2.0.0 \\\n'
+            b' --hash=sha256:abcd\n',
+        ),
+        (
+            b'a=2.0.0 \\\n --hash=sha256:abcd\nb==1.0.0\n',
+            PASS,
+            b'a=2.0.0 \\\n --hash=sha256:abcd\nb==1.0.0\n',
+        ),
     ),
 )
 def test_integration(input_s, expected_retval, output, tmpdir):

requirements-txt-fixer does not handle multiline dependencies
Given:
```
distlib==0.3.0 \
    --hash=sha256:2e166e231a26b36d6dfe35a48c4464346620f8645ed0ace01ee31822b288de21
appdirs==1.4.3 \
    --hash=sha256:9e5896d1372858f8dd3344faf4e5014d21849c756c8d5701f78f8a103b372d92 \
    --hash=sha256:d8b24664561d0d34ddfaec54636d502d7cea6e29c3eaf68f3df6180863e2166e
filelock==3.0.12 \
    --hash=sha256:18d82244ee114f543149c66a6e0c14e9c4f8a1044b5cdaadd0f82159d6a6ff59 \
    --hash=sha256:929b7d63ec5b7d6b71b0fa5ac14e030b3f70b75747cef1b10da9b879fef15836
```

requirements-txt-fixer will move all `--hash` lines on top of the file.
tests/requirements_txt_fixer_test.py::test_integration[b==1.0.0\nc=2.0.0 tests/requirements_txt_fixer_test.py::test_integration[a=2.0.0
tests/requirements_txt_fixer_test.py::test_integration[-0-] tests/requirements_txt_fixer_test.py::test_integration[\n-0-\n] tests/requirements_txt_fixer_test.py::test_integration[# tests/requirements_txt_fixer_test.py::test_integration[foo\n# tests/requirements_txt_fixer_test.py::test_integration[foo\nbar\n-1-bar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[bar\nfoo\n-0-bar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[a\nc\nb\n-1-a\nb\nc\n] tests/requirements_txt_fixer_test.py::test_integration[a\nc\nb-1-a\nb\nc\n] tests/requirements_txt_fixer_test.py::test_integration[a\nb\nc-1-a\nb\nc\n] tests/requirements_txt_fixer_test.py::test_integration[#comment1\nfoo\n#comment2\nbar\n-1-#comment2\nbar\n#comment1\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[#comment1\nbar\n#comment2\nfoo\n-0-#comment1\nbar\n#comment2\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[#comment\n\nfoo\nbar\n-1-#comment\n\nbar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[#comment\n\nbar\nfoo\n-0-#comment\n\nbar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[\nfoo\nbar\n-1-bar\n\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[\nbar\nfoo\n-0-\nbar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[pyramid==1\npyramid-foo==2\n-0-pyramid==1\npyramid-foo==2\n] tests/requirements_txt_fixer_test.py::test_integration[ocflib\nDjango\nPyMySQL\n-1-Django\nocflib\nPyMySQL\n] tests/requirements_txt_fixer_test.py::test_integration[-e tests/requirements_txt_fixer_test.py::test_integration[bar\npkg-resources==0.0.0\nfoo\n-1-bar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[foo\npkg-resources==0.0.0\nbar\n-1-bar\nfoo\n] tests/requirements_txt_fixer_test.py::test_integration[git+ssh://git_url@tag#egg=ocflib\nDjango\nijk\n-1-Django\nijk\ngit+ssh://git_url@tag#egg=ocflib\n] tests/requirements_txt_fixer_test.py::test_requirement_object