The dynamic thermal behavior of a bi-layered composite sphere due to a sudden temperature change on the outer surface is investigated. The analytical-numerical technique, which is based on the Laplace transformation and the Riemann-sum approximation, is employed to predict the temperature and heat flux histories in the composite sphere. The effects of different parameters such as the relaxation time, the thermal diffusivity ratio, the thermal conductivity ratio, the relaxation time ratio, and the radius ratio of the inner and outer layers of the composite sphere are studied and presented. (C) 2003 Elsevier Ltd. All rights reserved.