  We propose a candidate $c$-function in arbitrary dimensional quantum field
theories with broken Lorentz and rotational symmetry. For holographic theories
we derive the necessary and sufficient conditions on the geometric background
for these $c$-functions to satisfy the $c$-theorem. We obtain the null energy
conditions for anisotropic background to show that do not themselves assure the
$c$-theorem. By employing them, we find that is possible to impose conditions
on the UV data that are enough to guarantee at least one monotonic $c$-function
along the RG flow. These UV conditions can be used as building blocks for the
construction of anisotropic monotonic RG flows. Finally, we apply our results
to several known anisotropic theories and identify the region in the parameters
space of the metric where the $c$-theorem holds for our proposed $c$-function.
