diff --git a/stingray/base.py b/stingray/base.py
index 92fc14eef..8a851117f 100644
--- a/stingray/base.py
+++ b/stingray/base.py
@@ -387,6 +387,12 @@ def to_pandas(self) -> DataFrame:
         Array attributes (e.g. ``time``, ``pi``, ``energy``, etc. for
         ``EventList``) are converted into columns, while meta attributes
         (``mjdref``, ``gti``, etc.) are saved into the ``ds.attrs`` dictionary.
+
+        Since pandas does not support n-D data, multi-dimensional arrays are
+        converted into columns before the conversion, with names ``<colname>_dimN_M_K`` etc.
+
+        See documentation of `make_nd_into_arrays` for details.
+
         """
         from pandas import DataFrame
         from .utils import make_nd_into_arrays
@@ -423,6 +429,11 @@ def from_pandas(cls: Type[Tso], ts: DataFrame) -> Tso:
         using the standard attributes of the wanted StingrayObject (e.g.
         ``time``, ``pi``, etc. for ``EventList``)
 
+        Since pandas does not support n-D data, multi-dimensional arrays can be
+        specified as ``<colname>_dimN_M_K`` etc.
+
+        See documentation of `make_1d_arrays_into_nd` for details.
+
         """
         import re
         from .utils import make_1d_arrays_into_nd
diff --git a/stingray/utils.py b/stingray/utils.py
index 793520944..a78a62271 100644
--- a/stingray/utils.py
+++ b/stingray/utils.py
@@ -161,6 +161,8 @@ def any_complex_in_array(array):
 def make_nd_into_arrays(array: np.ndarray, label: str) -> dict:
     """If an array is n-dimensional, make it into many 1-dimensional arrays.
 
+    Call additional dimensions, e.g. ``_dimN_M``. See examples below.
+
     Parameters
     ----------
     array : `np.ndarray`
@@ -237,6 +239,8 @@ def get_dimensions_from_list_of_column_labels(labels: list, label: str) -> list:
 def make_1d_arrays_into_nd(data: dict, label: str) -> np.ndarray:
     """Literally the opposite of make_nd_into_arrays.
 
+    Call additional dimensions, e.g. ``_dimN_M``
+
     Parameters
     ----------
     data : dict