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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 satisfyingcertain size conditions. The aim of this paper is to study the endpointestimates of these commutators in the weighted Morrey spaces and in thegeneralized Morrey spaces, under the assumptions that $[b,\mathcalT_\alpha]~(0\leq\alpha<n)$ satisfy (weighted or unweighted) endpointinequalities on $\mathbb R^n$ and on bounded domains. Furthermore, asapplications of our main results, we will obtain, in the endpoint case, theboundedness properties of many important operators in classical harmonicanalysis on the weighted Morrey and the generalized Morrey spaces.

Endpoint estimates for commutators of sublinear operators in the Morrey type spaces