  We study Poincar\'e problem for a linear uniformly parabolic operator $\P$ in
a cylinder $Q=\Omega\times (0,T).$ The boundary operator $\B$ is defined by an
oblique derivative with respect to a tangential vector field $\l$ defined on
the lateral boundary $S.$ The coefficients of $\P$ are supposed to be $VMO$
away from the set of tangency $E$ and to possess higher regularity in $x$ near
to $E.$ A unique strong solvability result is obtained in $W^{2,1}_p(Q)$ for
all $p\in (1,\infty).$
