The existence and uniqueness of T-periodic solutions for the following p-Laplacian equations: $$({phi}_p(x^{prime}))^{prime}+{alpha}(t)x^{prime}+g(t,x)=e(t),;x(0)=x(T),x^{prime}(0)=x^{prime}(T)$$ are investigated, where ${phi}_p(u)={mid}u{mid}^{p-2}u$ with $p$ > 1 and ${alpha}{in}C^1$, $e{in}C$ are T-periodic and $g$ is continuous and T-periodic in $t$. By using coincidence degree theory, some existence and uniqueness results are obtained.