The semiclassical approximation of the coherent-state propagator requires the computation of complex trajectories satisfying special boundary conditions. In this paper we present a method for the determination of such trajectories for one-dimensional polynomial potentials. We also compute the semiclassical propagator for the case V(q) = lambda q(2)/2 + beta q(4) and compare the results with an ''exact'' calculation. (C) 1996 Academic Press, Inc.2522458478