The minimum propellant optimal rendezvous maneuver of two cosmic vehicles on circular and elliptical orbits is examined. It is assumed that the target without propulsion moves on an orbit around the Earth or other planets as a satellite, and the tracking vehicle with variable thrust propulsion moves on a close orbit. The problem of the determination of the optimal laws of variation which characterize the minimum propellant orbital rendezvous is formulated as an extremum variational problem with constraints, where the linear motion equations of the tracking vehicle are considered. On the basis of the optimal laws established in this manner numerical applications of practical interest are carried out.