This short paper gives two remarks on the singularities of the scattering amplitudes in a perturbation theory. First, it is pointed out that if the condition of stability is violated at several corners of a Feynmann diagram so that analytic extensions with respect to several external masses must be made, different sequences of carrying out the analytic extensions may lead to different positions of the singularities with respect to the final position of the integration contour (in a dispersion integral) and hence to different expressions for the amplitudes. Next, it is pointed out that the non-Landau singularities fall into two classes, of which one, say the first, is given by Cutkosky. For singularities in the first class, it is shown that they may be independent of the internal masses if and only if all the internal masses are equal or if the diagram is a loop. Their positions for the latter case are given. For singularities in the second class, it is shown that they are always independent of the internal masses and that they occur only for a very restricted set of diagrams.