The DOUG (domain decomposition on unstructured grids) package was first developed from 1996-1998 as a parallel solver for scalar elliptic PDEs discretised with finite elements. In this paper we describe its extension to unsymmetric elliptic systems of PDEs, highlighting software design and parallelisation issues. As an application we discuss the performance of the extended package applied to the incompressible Navier-Stokes equations, discretised with mixed finite elements. In particular we focus on discontinuous pressure elements, which are important in many practical applications. We also indicate briefly the application of this solver to Navier-Stokes stability assessment. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.