  In this paper, we study the stability of neckpinch singularities. We show
that if a mean curvature flow $\{M_t\}$ develops only finitely many neckpinch
singularities at the first singular time, then the mean curvature flow starting
at any sufficiently small perturbation of $M_0$ can also develop only neckpinch
type singularities at the first singular time. We also show stability of
nondegenerate neckpinch singularities in the above sense, which speaks in favor
of stability of Type I singularities.
