This is a review of the previous work conducted on the double-diffusive effect in viscosity stratified systems. Two configurations are considered which are supposed to be stable in the context of single-component flows. The flow in these configurations is shown to be unstable in the presence of double-diffusive effect. A new mode of instability due to the double-diffusive effect was found, and a rich variety of instability patterns are observed in the direct numerical simulations of such flows.