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In this paper, we discuss the conditions for a center for the generalized Liénard system $$\frac{\mathrm{d}x}{\mathrm{d}t}=\varphi \left(y\right)-F\left(x\right),\frac{\mathrm{d}y}{\mathrm{d}t}=-g\left(x\right),$$ or $$\frac{\mathrm{d}x}{\mathrm{d}t}=\psi \left(y\right),\frac{\mathrm{dy}}{\mathrm{d}t}=-f\left(x\right)h\left(y\right)-g\left(x\right),$$ with $f\left(x\right)$, $g\left(x\right)$, $\varphi \left(y\right)$, $\psi \left(y\right)$, $h\left(y\right)ℝ\to ℝ$, $F\left(x\right)={\int }_0^{x}f\left(x\right)\mathrm{d}x$, and $xg\left(x\right)>0$ 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].