  Let $[b,\mathcal T_\alpha]~(0\leq\alpha<n)$ be the commutators generated by
$BMO(\mathbb R^n)$ functions and a class of sublinear operators satisfying
certain size conditions. The aim of this paper is to study the endpoint
estimates of these commutators in the weighted Morrey spaces and in the
generalized Morrey spaces, under the assumptions that $[b,\mathcal
T_\alpha]~(0\leq\alpha<n)$ satisfy (weighted or unweighted) endpoint
inequalities on $\mathbb R^n$ and on bounded domains. Furthermore, as
applications of our main results, we will obtain, in the endpoint case, the
boundedness properties of many important operators in classical harmonic
analysis on the weighted Morrey and the generalized Morrey spaces.
