Three alternate-row intercrop experiments of sorghum (Sorghum bicolor)–cowpea (Vigna unguiculata) and/or millet (Pennisetum glaucum)–cowpea were grown at plant densities of 20 000 to 80 000 plants ha−1 at two locations in northern Nigeria between 1990 and 1992 to examine relations between yield and plant density. These relations were examined using the reciprocals of yield per plant to determine effects of environment, species and genotype on the theoretical maximum yield and optimum plant density. The intercrops were dominated by cereals, and cowpea biomass (BY) and seed yield (SY) were <10% of cereal BY and SY. Cowpea yields decreased as cereal plant density (D) increased, whereas cereal and total intercrop yields increased asymptotically with increasing D. Biomass yield of all intercrops responded to increasing D in a similar manner and the theoretical maximum intercrop BY was 12 290 kg ha−1 in all experiments. The response of SY to D varied among intercrops and was greatest and least with early and late maturing cereals respectively. The optimum D required to produce 90% maximum intercrop BY and SY varied between 15 600 and 30 000 plants ha−1, and 0 (no response to D) and 120 000 plants ha−1 respectively, and was higher for sorghum than for millet intercrops. The implications of these responses for agronomic management and germplasm improvement of cereal–cowpea intercrops are discussed.