We study the maximum and antimaximum principles for the p-Laplacian operator under Steklov boundary conditions with an indefinite weight −∆pu + |u| p−2 u = 0 in Ω, |∇u| p−2 ∂u ∂ν = λm(x)|u| p−2 u + h(x) on ∂Ω, where Ω is a smooth bounded domain of R N , N > 1. After reviewing some elementary properties of the principal eigenvalues of the p-Laplacian under Steklov boundary conditions with an indefinite weight, we investigate the maximum and antimaximum principles for this problem. Also we give a characterization for the interval of the validity of the uniform antimaximum principle. 2010 Mathematics Subject Classification. 35J70. Key words and phrases. p-Laplacian; Steklov boundary conditions: indefinite weight; maximum and antimaximum principles.