The authors provide interesting results regarding the existence and uniqueness of limit cycles for a class of second order differential equations of the form, \[ \dot{x}=y, \qquad \dot{y}=-|x|^m \operatorname{sgn}(x)-f(x,y)y, \tag{1} \] where \(1 \leq m < +\infty\) and \(f(x, y)\) is continuous in \(\mathbb{R}^2\). It is important to notice that system (1) contains the well known class of systems called van der Pol-Rayleigh oscillators. The paper possesses four main results concerning system (1): Theorem 1 states conditions for the uniqueness of a limit cycle; Theorem 2 states necessary conditions for the existence of a limit cycle; Theorem 3 provides a criterion for the existence of a limit cycle and; Theorem 4 provides a criterion for the non-existence of limit cycles. Using these four results the authors prove the uniqueness of limit cycles for three classes of the van der Pol-Rayleigh oscillators and they study their global dynamics in the Poincaré disc as well. Moreover, an interesting comparison between Theorem 1 and some known results is done. The authors show that a result proved by J. L. Massera [Boll. Unione Mat. Ital., III. Ser. 9, 367–369 (1954; Zbl 0057.07004)] can be obtained directly from Theorem 1. On the other hand they point out that Theorem 1 is weaker than a conjecture proposed by A. de Castro [Boll. Unione Mat. Ital., III. Ser. 9, 280–282 (1954; Zbl 0056.08301)].