Abstract
Pseudo-symmetries were introduced by Sarlet and Cantrijn (1984) for time-dependent non-conservative systems. They are reconsidered in the context of general autonomous second-order systems, relying on the new approach to such systems which was presented by Sarlet et al. They further introduce the notion of adjoint symmetries of a second-order system, as being associated to invariant 1-forms, and show how they may be related to first integrals or to Lagrangians under appropriate circumstances. Their results enable them to clarify a rather unusual account of Noether's theorem which was recently given by Gordon (1986).