This paper is devoted to the study of systems of \(p\)-Laplacian type \[ -(\|x'(t)\|^{p-2} x'(t))'+ f(t, x(t), x'(t))= 0 \] submitted to single-valued or multi-valued periodic-type boundary conditions. The existence of periodic solutions is proved, using a combination of maximal monotonicity and topological degree, under some assumptions too lengthy to be explicited here. The scalar case with nonlinear boundary conditions is considered as well. The obtained results partially extend earlier ones of Hartman, Knobloch, Mawhin, Guo, Zhang, Boccardo-Drabek-Giachetti-Kucera, del Pino-Elgueta-Manásevich.