When multiple independent robot arms attempt to perform concurrent operations at the same work cell, spatial interference imposes limits on the degree of parallelism that can be achieved. It is shown that as the number of independent arms approaches infinity, the degree of parallelism is bounded. Mathematical limiting values are derived for the extent of parallelism for two cases of an idealized simplistic application. The main value of these results is to demonstrate that under conditions of spatial contention, there is little merit in having more than two independent arms at a work cell. Designing the work cell to reduce contention increases the value of multiple independent arms. © 1985.