We compare simultaneous versus sequential moves in R&D decisions within an asymmetric R&D/Cournot model with linear demand (for differentiated products), general R&D costs, and spillovers. Simultaneous play and sequential play (with and without a specified leader) can emerge as appropriate formulations, depending on the ratios of spillover rate over demand cross-slope, but not on R&D efficiency. When at least one ratio is above 1/2, a sequential solution mitigates competition and leads to higher profits for each firm, and to higher social welfare. When uniquely specified, the stronger firm emerges as the R&D first-mover