A mathematical apparatus for studying interdiffusion in three-component systems, using a theoretical approach similar to that previously proposed for describing interdiffusion in binary alloys, has been developed. This approach takes into account the active role of vacancies without assuming their equilibrium distribution; therefore, the equations for component fluxes contain contributions due to the vacancy density gradient. Solutions of a linearized system of interrelated diffusion equations for three components and vacancies are obtained. It has been found that the time dependences of the component density distributions in the diffusion zone, up to terms having a higher order in the expansion in powers of the vacancy concentration, are determined by two coefficients of interdiffusion. These coefficients depend nonlinearly on the component concentrations and the self-diffusion coefficients.