Non-linear gravitational clustering in a universe dominated by dark energy, modelled by a `quintessence' scalar field, and cold dark matter with spacetime varying mass is studied. Models of this type, where the variable mass is induced by dependence on the scalar field, as suggested by string theory or extra dimensions, have been proposed as a viable solution of the coincidence problem. A general framework for the study of the non-linear phases of structure formation in scalar field cosmologies is provided, starting from a general relativistic treatment of the combined dark matter–dark energy system. As a first application, the mildly non-linear evolution of dark matter perturbations is obtained by a straightforward extension of the Zel'dovich approximation. We argue that the dark energy fluctuations may play an active role in cosmological structure formation if the scalar field effective potential develops a temporary spinodal instability during the evolution.