The mass and energy expended during the transfer of a space vehicle from one orbit to another depend both on the magnitude of the orbital change and on the spacecraft propulsion variables. In the present paper the optimum time behaviour of these variables is investigated: that is, those functions which maximize the residual mass of the spacecraft, or which minimize the total energy required for a given total equivalent velocity change. It is found that an optimum relation exists between the flow of mass and of energy, and that, provided this condition is satisfied, the results depend only on the total energy supplied, and not on the way it is released. The optimum functions and maximum mass ratios derived in the paper apply in the general case where the efficiency of the propulsion system varies with exhaust velocity, and when the ejected mass possesses intrinsic energy in addition to that supplied from a separate source. Formulae are also developed for the maximization of the useful or disposable mass, and various examples are given.