We derive global existence and uniqueness of solutions for the Lifshitz-Sly
ozov system, which appears in the modelling of precipitation from supersatu
rated solutions. Mathematically, the system consists of a transport equatio
n for the density function, coupled to an integral equation which expresses
conservation of the total mass. The existence is obtained by a fixed-point
technique, based on the expression of the density function in terms of the
monomer concentration, as given by the method of characteristics. For some
particular cases we obtain an explicit expression of the solution by using
the Laplace transform. Finally, in some more general cases, we prove, if a
solution exists, convergence to a stationary solution for large times. AMS
classification scheme numbers: 35, 82.