A theoretical study is performed of the multimode dynamics and steady-state transverse-mode selection in vertical-cavity surface-emitting lasers subject to weak optical feedback in an external-cavity configuration. Attention is focused on the competition between the two lowest-order modes (LP(01) and LP(11) degenerate modes) appropriate to the chosen circularly symmetric vertical-cavity surface-emitting laser structure. It is shown that preferential excitation of either mode can be effected by appropriate choice of optical feedback delay. Opportunities for enhancing modal discrimination by adjusting the strength of optical feedback are also presented. (C) 1996 Optical Society of America.