Let { S ( t ) : t > 0 } \{ S(t):t > 0\} be a nonlinear semigroup of operators mapping a closed subset C C of a real Banach space X X into itself. Conditions are found for an accretive operator in X X to be the generator of { S ( t ) : t > 0 } \{ S(t):t > 0\} with smoothing effect: For each \[ x ∈ C , S ( t ) x ∈ V a .e . t > 0, x \in C,\;S(t)x \in V\;{\text {a}}{\text {.e}}{\text {.}}\;{\text {t > 0,}} \] among other things, where V V is a Banach space imbedded continuously in X X . The conditions contain a Gårding-type inequality, and are shown also to be necessary if C C is a closed convex subset of a "nice" Banach space X X .