  Given a semiclassical distribution $f_h$ microlocalized on a Lagrangian
manifold $\Lambda_0$, $H\in C^\infty( T^\ast {\bf R}^n)$, and $H=E$ a regular
energy surface, we find asymptotic solutions of the PDE $(H(x,\widehat{p})-E)
\, u_h (x,E)=f_h(x)$ in terms of the Maslov canonical operator, when the
Hamilton vector field $v_H$ fails to be transverse to $\Lambda_0$ at some
points.
