In this paper, we consider a two-species fishery model where the species can have different biological interactions, namely, competitive, symbiotic or prey-predator relationship. Each species is harvested by a group of fisherpersons. We characterize and compare equilibrium harvesting strategies, steady-state stocks and total discounted utilities under different modes of play, that is, noncooperation in both groups, cooperation in each of the groups and cooperation in only one group of fisherpersons. Our main results are as follows: (i) In all scenarios, the equilibrium strategy of a player fishing either species consists of harvesting, in each period, a proportion of the available stock. (ii) The dividend of cooperation in a given group is increasing with the number of players in that group. (iii) Coordination between players in a given group may be detrimental (biologically and economically) to the other species.