The work is devoted to the non-linear dynamic stability of heterogeneous orthotropic truncated conical shells subjected to the combined static and time-dependent axial loads. The basic equations are derived using the finite deflection theory with von Karman-Donnell-type of kinematic non-linearity and reduced to a non-linear differential equation with the time variable coefficient using the superposition principle and Galerkin method. The resulting equation is solved numerically using Runge-Kutta method for variety of an axial loading speed, heterogeneity of features, orthotropic material properties and conical shell characteristics to obtain the non-linear critical time parameters. Finally, the influences of the axial loading speed, non-linearity, heterogeneity and orthotropy on the dimensionless critical time parameters are discussed in detail. (C) 2015 Elsevier Ltd. All rights reserved.