Abstract: First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x₀,y₀,z₀∈ K, compute sequences x_n,y_n,z_n such that ... . For η,ρ,γ > 0 are constants,{α_n},{β_n},{a_n},{r_n},{δ_n},{λ_n} - [0,1], {u_n},{v_n},{ω_n} are sequences in K, and 0 ≤α_n+r_n ≤ 1,0 ≤β_n+δ_n≤ 1,0 ≤ a_n+λ_n≤ 1,-n ≥ 0, where T : K → H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems. 

Key words: two-step model, general three-step model, system of strongly monotonic nonlinear variational inequalities, projection formulas, convergence of three-projection method