  In this paper we show that condition $\operatorname{Sub_r}(\Psi)$ on the
subprincipal symbol is sufficient for local solvability of pseudodifferential
operators of real subprincipal type. These are the operators having real
principal symbol which vanish on an involutive manifold where the subprincipal
symbol is of principal type. This condition has previously been shown by the
author to be necessary for local solvability of pseudodifferential operators of
real subprincipal type.
