The BRST-antiBRST invariant path integral formulation of classical mechanics of Gozzi et al is generalized to pseudomechanics. It is shown that projections to physical propagators may be obtained by BRST-antiBRST invariant boundary conditions. The formulation is also viewed from recent group theoretical results within BRST-antiBRST invariant theories. A natural bracket expressed in terms of BRST and antiBRST charges in the extended formulation is shown to be equal to the Poisson bracket. Several remarks on the operator formulation are made.