Let $ar{M}$ be a smoothly bounded pseudoconvex complex manifold with a family of almost complex structures ${L^{ au}}_{{ au}{in}I}$, $0{in}I$, which extend smoothly up to bM, the boundary of M, and assume that there is ${lambda}{in}C^{infty}$(bM) which is strictly subharmonic with respect to the structure $L^0|_{bM}$ in any direction where the Levi-form vanishes on bM. We obtain explicit estimates for the $ar{partial}$-Neumann problem in Sobolev spaces both in space and parameter variables. Also we get a similar result when $ar{M}$ is strongly pseudoconvex.