In this study, we have theoretically investigated the effect of parallel superposition of modulation on the stability of two layer Newtonian and viscoelastic flows down an inclined plane and it has been demonstrated that dynamic modulation can be used to influence the interfacial stability of Newtonian and viscoelastic fluids down an inclined plane. In general, for small and O(1) Reynolds numbers, the effect of dynamic modulation on the interfacial stability of viscoelastic flows is much more pronounced, however, relatively large modulation amplitudes are required to achieve significant stabilization/destabilization. Moreover, it has been demonstrated that the influence of dynamic modulation on the stability of the interfacial mode is relatively insensitive to the inclination angle and the disturbance wavenumber. In addition, it has been shown that for Newtonian flows one cannot establish a relationship between the most effective modulation frequencies and the inertial time scales of the flow (i.e. 1/Re-1, 1/Re-2 or 1/(\Re-1 - Re-2\) or the frequency of the most dangerous interfacial mode in absence of modulations. Similarly, for viscoelastic hows at small and O(1) Re, no clear connection between the most stabilizing or destabilizing modulation frequencies and the fluid time scales have been established (i.e. 1/We(1), 1/We(2) or 1/\We(1) - We(2)\). Finally, it has been shown that the mechanism of purely elastic and inertial interfacial instabilities in multilayer flows down an inclined plane is unchanged in the presence of dynamic modulation. (C) 2001 Elsevier Science B.V. All rights reserved.