We report on the time evolution of the aggregation behaviour of cationic liposome-polyelectrolyte complexes studied by means of dynamic light scattering technique. Pure dioleoyltrimethilammoniumpropane (DOTAP) and mixed DOTAP-dipalmitoylphosphatidylcholine (DPPC) liposomes in polyacrylate sodium salt aqueous solutions in a wide concentration range have been investigated and the size and size distributions of the resulting aggregates evaluated from the intensity autocorrelation function of the scattered light. Under appropriate conditions, we found two discrete aggregation regimes, resulting in two different structural arrangements, whose time evolution depends on the charge ratio and the polyelectrolyte molecular weight. A first small component of average size in the 100-500 range nm coexists with a larger component, whose typical size increases with time, up to some micrometers. The cluster growth from a single liposome, 70 nm in diameter, to the formation of polymer-coated liposome aggregates has been briefly discussed in the light of steric stabilization of colloids. Moreover, it has been found that the kinetics of aggregation of the larger, time-dependent, component follows a dynamical scaling within the diffusion-limited cluster aggregation (DLCA) regime. The understanding of structures resulting from interactions between polyelectrolytes with oppositely charged liposomes may help towards formulation of "lipoplexes" (cationic lipid-DNA complexes) to use as non-viral gene carriers.