A Hamiltonian framework of non-equilibrium thermodynamics is adopted to construct a set of dynamical continuum equations for a polymer blend with matrix viscoelasticity and a narrow droplet size distribution that is assumed to obey a Weibull distribution function. The microstructure of the matrix is described in terms of a conformation tensor. The variable droplet distribution is described in terms of two thermodynamic variables: the droplet shape tensor and the number density of representative droplets. A Hamiltonian functional in terms of the thermodynamic variables is introduced and a set of time evolution equations for the system variables is derived. Sample calculations for homogenous flows and constant droplet distribution are compared with data of a PIB/PDMS blend and a HPC/PDMS blend with high viscoelastic contrast. For the PIB/PDMS blend, satisfactory predictions of the flow curves are obtained. Sample calculations for a blend with variable droplet distribution are performed and the effect of flow on the theology, droplet morphology, and on the droplet distribution are discussed. It is found that deformation can increase or decrease the dispersity of the droplet morphology for the flows investigated herein. (C) 2004 Elsevier B.V. All rights reserved.