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We investigate the following nonlinear equations with p-Laplacian-like operators (φ(x′(t)))′+f(x(t))x′(t)+g(x(t))=e(t): some criteria to guarantee the existence and uniqueness of periodic solutions of the above equation are given by using Mawhin's continuation theorem. Our results are new and extend some recent results due to Liu (B. Liu, Existence and uniqueness of periodic solutions for a kind of Lienard type p-Laplacian equation, Nonlinear Analysis TMA, 69, 724–729, 2008).