It has been claimed that rotation of neuronal population vectors in the primary motor cortex during tasks involving transformation of movement directions provides direct evidence that a mental rotation algorithm is being used. An alternative explanation offered here, the 'asynchronous superposition hypothesis', asserts that the apparent rotation can result from the summation of two stationary vectors, one in the stimulus direction and one in the target movement direction, which vary in length over time. Computer simulations demonstrate the surprising result that the asynchronous superposition hypothesis can produce activation of motor corex cells with intermediate preferred directions, something previously assumed to confirm a mental rotation algorithm. Simulations also demonstrate that the asynchronous superposition hypothesis accounts for some aspects of the data more naturally than does an explanation based on a mental rotation algorithm, and suggest experimental tests that can distinguish between these two hypotheses.