  Non-linear gravitational clustering in a universe dominated by dark energy,
modelled by a `quintessence' scalar field, and cold dark matter with space-time
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.
