Kooij and Sun (J Math Anal Appl 208:260-276, 1997) proposed a theorem to guarantee the uniqueness of limit cycles for the generalized Liénard system dx/dt = h(y) − F(x), dy/dt = −g(x). We will give a counterexample to their theorem. Moreover, we shall give some sufficient conditions for the existence, uniqueness and hyperbolicity of limit cycles. Keywords Generalized Liénard systems • Limit cycle • Uniqueness • Hyperbolicity where the functions in (1) are assumed to be continuous and such that uniqueness for solutions of initial value problems is guaranteed. We define, as usual, G(x) := x 0 g(s)ds and H (y) := y 0 h(s)ds. Huang and Sun [8] have shown a theorem to B Ping Yan