A two-species predator-prey system of Lotka-Volterra type that includes harvesting terms, can have four equilibria in the positive quadrant. In this paper, it is assumed that all the parameters of such a system are positive
-periodic continuous functions. The authors make use of Mawhin’s continuation theorem of coincidence degree theory to prove that, under certain inequality assumptions on the periodic parameters, there exist (at least) four
-periodic solutions of the given system. Finally, a numerical example of such a system is presented that satisfies all the assumptions of the theorem.