Summary: This paper deals with the question of uniqueness of limit cycles in predator-prey systems of Gause type. By utilizing several transformations, these systems are reduced to a generalized Lienard system as discussed by L. A. Cherkas
and L. I. Zhilevich
[Differ. Uravn. 6, 1170-1178 (1970; Zbl 0213.364
)] and by Z. Zhang
[Appl. Anal. 23, 63-76 (1986; Zbl 0582.34038
)]. As a consequence, criteria for the uniqueness of limit cycles are derived, which include results of K.-S. Cheng
[SIAM J. Math. Anal. 12, 541-548 (1981; Zbl 0471.92021
)] and are related to results of L.-P. Liou and K.-S. Cheng (to appear). Several examples are given to illustrate our results.