The development of unsteady mixed convection flow of an incompressible laminar viscous fluid over a vertical cone has been investigated when the fluid in the external stream is set into motion impulsively, and at the same time the surface temperature is suddenly changed from its ambient temperature. The problem is formulated in such a way that at t = 0, it reduces to Rayleigh type of equation and as t → ∞, it tends to Falkner-Skan type of equation. The scale of time has been selected such that the traditional infinite region of integration become finite which significantly reduce the computational time. The coupled non-linear partial differential equations governing the unsteady mixed convection flow have been solved numerically by using an implicit finite-difference scheme in combination with the quasi-linearization technique. There is a smooth transition from the initial steady state to the final steady state. The velocity, temperature, and concentration profiles and their gradients at the surface for various values of the governing parameters are reported in the present study. © 2006 Elsevier Ltd. All rights reserved.