The cosmogenic radionuclides, (sup 10)Be (1.5 Ma), (sup 26)Al (0.705 Ma), (sup 36)Cl (0.301 Ma), and (sup 53)Mn (3.7 Ma) were measured in selected clasts and matrix samples from the howardite Kapoeta. This work is an extension of that based on (sup 10)Be and (sup 26)Al (1). Recent work based on measurements of cosmogenic (sup 21)Ne suggest the possibility of a complex recent exposure history for Kapoeta. The measurement of these radionuclides, in conjunction with production rates based on Monte Carlo calculations, can constrain exposure conditions and durations. Taken together, the radionuclide data are entirely consistent with a single stage 4(pi) exposure lasting (approximately) 3 Ma.