We extend Henry Poincaré's normal form theory for autonomous difference equations x_κ+1 = f(x_κ) to nonautonomous difference equations x_κ+1 = f_κ(x_κ). Poincaré's nonresonance condition λ_j - Π_i=1ⁿ λ_i^qi ≠ 0 for eigenvalues is generalized to the new nonresonance condition λ_j ∩ Π_i=1ⁿ λ_i^qi = Ø for spectral intervals.