Reiterated homogenization is studied for divergence structure parabolic problems of the form ∂uε ∂t − div a x ε , x ε2 , t, Duε = f . It is shown that under standard assumptions on the function a (y1, y2, t, ξ) the sequence {uε} of solutions converges weakly in L p(0, T ;W1,p 0 (Ω)) to the solution u of the homogenized problem ∂u ∂t − div (b (t, Du)) = f