  We consider the running of the neutrino mass matrix in the Standard Model and
the Minimal Supersymmetric Standard Model, extended by heavy singlet Majorana
neutrinos. Unlike previous studies, we do not assume that all of the heavy mass
eigenvalues are degenerate. This leads to various effective theories when the
heavy degrees of freedom are integrated out successively. We calculate the
Renormalization Group Equations that govern the evolution of the neutrino mass
matrix in these effective theories. We show that an appropriate treatment of
the singlet mass scales can yield a substantially different result compared to
integrating out the singlets at a common intermediate scale.
