An effective approach for the solution of the inverse problems associated with EEG and MEG was introduced. It yields a complete answer to the non-uniqueness question even in the case of an arbitrary geometry. Furthermore, in the particular cases of spherical and ellipsoidal geometry it yields effective formulae for the ldquovisiblerdquo component of the current. The analysis is concerned with a continuously distributed current that can be reconstructed; the opposite case where the current is localized in a finite number of points, i.e. the case of a collection of dipoles is analyzed for spherical and ellipsoidal geometries respectively.