The authors study the limit cycles of the family of planar vector fields given by \[ \dot x=y, \quad \dot y = -g(x)-f(x,y)y, \] which has as a special case, when \(f(x,y)=f(x)\), the class of Liénard systems. The paper has two main results. The first one provides sufficient conditions for the system to have at most one limit cycle and, when it exists, provides also its stability. The second main result provides sufficient conditions for the system to have at least one limit cycle. In both cases, the functions \(f\) and \(g\) needs only to be continuous and Lipschitz continuous, respectively. In particular, the system needs not to be continuously differentiable. The authors also apply their results to the van der Pol-Duffing-Rayleigh oscillator \[ \dot x=y, \quad \dot y = -x-x^3-\varepsilon(b+x^2+ay^2)y, \] and on the asymmetric and nonsmooth van der Pol-Rayleigh oscillator \[ \dot x=y, \quad \dot y = -g(x)-\varepsilon(b+x^2+ay^2)y, \] where \[ g(x)=\begin{cases} rx, \text{ if } x\geqslant 0, \\ lx, \text{ if } x<0. \end{cases} \] In booth cases they obtain sufficient conditions for the existence of a unique limit cycle. Moreover, the authors study the stability and position of the limit cycle on the plane.