A linear partial differential equation of the form \(L(z,\partial_ z)u(z)=f(z)\), where \(u\) may be singular on \(K\), and where \(f\) is holomorphic in \(\Omega=(z\in C^{n+1};| z|\leq R)\), and \(K\) is a connected nonsingular complex hypersurface in \(\Omega\). They first give an integral representation of solutions singular on \(K\). Secondly they show that \(u(z)\) is holomorphic at \(K\) if \(u(z)\) has some growth properties near \(K\) under certain conditions on the differential operator \(L(z,\partial_ z)\).