diff --git a/xarray/core/missing.py b/xarray/core/missing.py
index e6dd8b537a0..ac0cbe1e702 100644
--- a/xarray/core/missing.py
+++ b/xarray/core/missing.py
@@ -460,6 +460,8 @@ def _get_interpolator(method, vectorizeable_only=False, **kwargs):
         "quadratic",
         "cubic",
         "polynomial",
+        "previous",
+        "next",
     ]
     valid_methods = interp1d_methods + [
         "barycentric",
@@ -596,7 +598,7 @@ def interp(var, indexes_coords, method, **kwargs):
         Note that all the coordinates should be Variable objects.
     method : string
         One of {'linear', 'nearest', 'zero', 'slinear', 'quadratic',
-        'cubic'}. For multidimensional interpolation, only
+        'cubic', 'previous', 'next'}. For multidimensional interpolation, only
         {'linear', 'nearest'} can be used.
     **kwargs
         keyword arguments to be passed to scipy.interpolate
diff --git a/xarray/tests/test_missing.py b/xarray/tests/test_missing.py
index 2ab3508b667..71c1fb0e5ad 100644
--- a/xarray/tests/test_missing.py
+++ b/xarray/tests/test_missing.py
@@ -92,7 +92,16 @@ def make_interpolate_example_data(shape, frac_nan, seed=12345, non_uniform=False
 def test_interpolate_pd_compat():
     shapes = [(8, 8), (1, 20), (20, 1), (100, 100)]
     frac_nans = [0, 0.5, 1]
-    methods = ["linear", "nearest", "zero", "slinear", "quadratic", "cubic"]
+    methods = [
+        "linear",
+        "nearest",
+        "zero",
+        "slinear",
+        "quadratic",
+        "cubic",
+        # "next",
+        # "previous",
+    ]
 
     for (shape, frac_nan, method) in itertools.product(shapes, frac_nans, methods):
 
@@ -291,7 +300,16 @@ def test_interpolate_limits():
 
 @requires_scipy
 def test_interpolate_methods():
-    for method in ["linear", "nearest", "zero", "slinear", "quadratic", "cubic"]:
+    for method in [
+        "linear",
+        "nearest",
+        "zero",
+        "slinear",
+        "quadratic",
+        "cubic",
+        "previous",
+        "next",
+    ]:
         kwargs = {}
         da = xr.DataArray(
             np.array([0, 1, 2, np.nan, np.nan, np.nan, 6, 7, 8], dtype=np.float64),