[en] An increase in both the luminosity and energy of colliding-beam accelerators beyond those contemplated at the present time, whilst keeping within practicable limits of power consumption, clearly implies stringent limits on efficiency and beam quality. Additional constraints necessary to limit the effects of beam distruption and ''beamstrahlung'' (synchrotron radiation arising from the collision process) have a more subtle influence. The essential features of these effects and the constraints on the different parameters involved are set out here in a simple and general way. Specific accelerating concepts are not discussed, but some criteria are indicated by which they can be assessed. Directions are suggested in which development and inventive thought might be profitable. (orig.)