The influence of solute-solute interactions on segregation processes in multi-component solid solutions leading to the formation of a new phase with a given stoichiometric composition, has been investigated for the first time. Expressions for the nucleation and growth rates have been derived. Estimates were developed for the time required to establish a steady-state nucleation rate in the system and the time interval for which such a steady-state can be sustained. Based on these results, it is anticipated that a method for an experimental determination of the parameters describing the interaction of the solute components, could be developed. The kinetic equation describing the evolution of the cluster size distribution function has been generalized to account for stochastic effects due to both fluctuations in the growth rate and possible spatial correlations of the evolving clusters in the matrix. The possible influence of such stochastic effects (thermal noise and random coalescence) on coarsening described by such additional terms has been discussed briefly.