A phenomenological model for the dynamics of a single drop immersed in an immiscible matrix is examined, the two incompressible component liquids being in general viscoelastic. Drop shape is assumed to be ellipsoidal. Transient predictions upon flow start-up are compared with experimental data in two different flow fields, for the case of a Newtonian drop in a viscoelastic matrix. Shear flow data are obtained from experiments performed in a parallel plate apparatus, by using a Boger fluid as the continuous phase. Planar elongation data are taken from the literature. The phenomenological model is also tested by comparing its predictions with finite element simulations found in the literature based on Oldroyd fluids. Model predictions are in general good agreement both with experiments and simulations. (c) 2004 Elsevier B.V. All rights reserved.