In this paper, we discuss the conditions for a center for the generalized Liénard system \[ \frac {{\rm d}x}{{\rm d}t}=\varphi (y)-F(x), \qquad \frac {{\rm d}y}{{\rm d}t}=-g(x), \] or \[ \frac {{\rm d}x}{{\rm d}t}=\psi (y), \qquad \frac {{\rm dy}}{{\rm d}t}= -f(x)h(y)-g(x),
\] with $f(x)$, $g(x)$, $\varphi (y)$, $\psi (y)$, $h(y)\: \mathbb R\rightarrow \mathbb R$, $F(x)=\int _0^xf(x)\mathrm{d}x$, and $xg(x)>0$ for $x\ne 0$. By using a different technique, that is, by introducing auxiliary systems and using the differential inquality theorem, we are able to generalize and improve some results in [1], [2].