Propagation of hypersound in a semiconductor superlattice in the presence of an external electric field of the form E=E₀+E₁ cos( omega t) has been studied theoretically. The analytical expressions obtained for the absorption coefficient are presented graphically. It is observed that in the absence of an AC electric field the dependence of Gamma on E₀ is non-linear unlike the homogeneous bulk material where the dependence of Gamma on E₀ is linear. The inclusion of an AC electric field affects the relation between Gamma and E₀ depending on the values of E₁ and omega tau . For a given E₁, the peaks of the curve of Gamma against E₀ decrease, shift and eventually oscillate for increasing values of omega tau , i.e. from or <<1 to omega tau >>1.