This paper identifies a number of key issues regarding the development of general modelling languages for combined lumped and distributed parameter processes, and proposes one such language. The latter has been implemented in the gPROMS process modelling system and permits the mathematical modelling of arbitrarily complex unit operations that are distributed over rectangular domains in terms of mixed systems of integral, partial differential, and algebraic equations (IPDAEs). Following language translation, validation and analysis, the method of lines is employed automatically to convert the IPDAEs to sets of ordinary differential-algebraic equations (DAEs). The latter are then solved simultaneously with the DAEs that model the behaviour of the lumped parameter units in the process. Three examples are presented to illustrate the capability of the proposed modelling system to deal with a wide variety of complex processes described in terms of IPDAEs.