diff --git a/.disabled-travis.yml b/.disabled-travis.yml
index 8638059e0ab..1569758168d 100644
--- a/.disabled-travis.yml
+++ b/.disabled-travis.yml
@@ -111,6 +111,31 @@ jobs:
            INSTALL_HOLE="false"
            CODECOV="true" SETUP_CMD="${PYTEST_FLAGS} --cov=MDAnalysis"
 
+    - os: linux
+      language: python
+      arch: arm64-graviton2
+      python:
+        - "3.7"
+      dist: focal
+      virt: vm
+      group: edge
+      before_install:
+        - python -m pip install cython numpy
+        # special test SciPy wheel for ARM64:
+        - python -m pip install https://anaconda.org/multibuild-wheels-staging/scipy/1.6.0.dev0+a240c17/download/scipy-1.6.0.dev0+a240c17-cp37-cp37m-manylinux2014_aarch64.whl
+        - python -m pip install --no-build-isolation hypothesis matplotlib pytest pytest-cov pytest-xdist tqdm
+      install:
+        - cd package
+        - python setup.py install
+        - cd ../testsuite
+        - python setup.py install
+        - cd ..
+      script:
+        - cd testsuite
+        - python -m pytest ./MDAnalysisTests --disable-pytest-warnings -n 8 -rsx --cov=MDAnalysis
+      after_success:
+        - echo "Override this stage for ARM64"
+
   allow_failures:
     - env: NUMPY_VERSION=dev EVENT_TYPE="cron"
 
diff --git a/package/setup.py b/package/setup.py
index e48e12c52e2..c5fc43675d9 100755
--- a/package/setup.py
+++ b/package/setup.py
@@ -268,8 +268,15 @@ def extensions(config):
     use_cython = config.get('use_cython', default=not is_release)
     use_openmp = config.get('use_openmp', default=True)
 
-    extra_compile_args = ['-std=c99', '-ffast-math', '-O3', '-funroll-loops',
-                          '-fsigned-zeros']  # see #2722
+    if platform.machine() == 'aarch64':
+        # reduce optimization level for ARM64 machines
+        # because of issues with test failures sourcing to:
+        # MDAnalysis/analysis/encore/clustering/src/ap.c
+        extra_compile_args = ['-std=c99', '-ffast-math', '-O1', '-funroll-loops',
+                              '-fsigned-zeros']
+    else:
+        extra_compile_args = ['-std=c99', '-ffast-math', '-O3', '-funroll-loops',
+                              '-fsigned-zeros']  # see #2722
     define_macros = []
     if config.get('debug_cflags', default=False):
         extra_compile_args.extend(['-Wall', '-pedantic'])
diff --git a/testsuite/MDAnalysisTests/formats/test_libdcd.py b/testsuite/MDAnalysisTests/formats/test_libdcd.py
index 0028a80bd3b..240aee1a74e 100644
--- a/testsuite/MDAnalysisTests/formats/test_libdcd.py
+++ b/testsuite/MDAnalysisTests/formats/test_libdcd.py
@@ -22,6 +22,7 @@
 import sys
 import string
 import struct
+import platform
 
 import hypothesis.strategies as strategies
 from hypothesis import example, given
@@ -317,8 +318,10 @@ def write_dcd(in_name, out_name, remarks='testing', header=None):
             f_out.write(xyz=frame.xyz, box=frame.unitcell)
 
 
-@pytest.mark.xfail(os.name == 'nt' and sys.maxsize <= 2**32,
-                   reason="occasional fail on 32-bit windows")
+@pytest.mark.xfail((os.name == 'nt'
+                    and sys.maxsize <= 2**32) or
+                    platform.machine() == 'aarch64',
+                   reason="occasional fail on 32-bit windows and ARM")
 @given(remarks=strategies.text(
     alphabet=string.printable, min_size=0,
     max_size=239))  # handle the printable ASCII strings