Let f ∈ C[−ω, ω], 0 < ω < π, be nonlinear and nondecreasing. We wish to estimate the degree of approximation of f by trigonometric polynomials that are nondecreasing in [−ω, ω]. We obtain estimates involving the second modulus of smoothness of f and show that one in general cannot have estimates with the third modulus of smoothness.