Polyelectrolyte "complexes" have been studied for almost a century and find more and more applications in cosmetics and DNA transfection. Most of the available studies focused on the thermodynamic aspects of the "complex" formation, mainly to determine phase diagrams and the influence of diverse physicochemical aspects on the formation of "complexes", but conversely less effort has been given to the kinetics of such processes. We describe herein the "complexation" kinetics of a short linear sodium polyphosphate (PSP) with poly(allylamine hydrochloride) (PAH) in the presence of 10 mM, 0.15 M and 1 M NaCl. We find, by using a combination of physicochemical techniques, that mixtures containing a 1 to 1 molar ratio of phosphate and amino groups allow the formation of "complexes" having a few 100 nm in diameter which progressively grow to particles up to 1.5 microns in hydrodynamic diameter, the growth process being accompanied by some progressive sedimentation. During this slow aggregation kinetics, the polyelectrolytes undergo a release of counterions and the zeta potential changes from a positive value to a negative one of -20 mV which is close to the zeta potential of (PSP-PAH)(n) films deposited under identical physicochemical conditions. Even though the complexes have a negative electrophoretic mobility, they contain an equimolar amount of amino and phosphate groups. This allows us to make some assumption about the structure of such "complexes" and to compare them with other published structures. We will also compare them with the aggregates found during the "layer-by-layer" deposition of the same species under the same conditions.