Consider two systems of differential equations (*) \(\dot x=y\), \(\dot y=- g(x)-\lambda f(x,y,v)y\) where \(v=y^ 2+\int^{x}_{0}g(s)ds\), \(\lambda >0\) and the system (\(\mu)\) \(\dot x=y\), \(\dot y=-g(x)-\lambda f(x,y,\mu)y\) with \(\mu \geq 0\). The problem of existence of closed trajectories for the system (*) and the system (\(\mu)\) is considered.