Properties of generalized solutions of model nonlinear elliptic systems of second order are studied in the semiball B₁⁺ = B ₁(0)∩{x_n > 0} ⊂ ℝⁿ, with the oblique derivative type boundary condition on Γ₁ = B ₁(0)∩{x_n = 0}. For solutions u ∈ H ¹(B₁⁺) of systems of the form d/dx _α a_α^k(u_x) = 0, k ≤ N, it is proved that the derivatives u_x are Hölder in B ₁⁺ ∪ Γ₁)\∑, where H _n-p(∑) = 0, p > 2. It is shown for continuous solutions u from H¹ (B₁⁺) of systems d/dx_α a_α^k (u,u_x) = 0 that the derivatives u_x are Hölder on the set (B₁⁺ ∪Γ₁)\∑, dim_H ∑ ≤ n - 2.