Abstract: We investigate the spectral theory for the system \(Ju’+qu=w(\lambda u+f)\) of ordinary differential equations where \(J\) is constant invertible skew-hermitian matrix while \(q\) is a hermitian and \(w\) a non-negative matrix whose entries are distributions of order \(0\). A major obstacle is the fact that, in general, the unique continuation of solutions of the differential equation is not possible. Basic information on distributions will be provided.