In double stars in young stellar objects, a protoplanetary disk is formed around each star, accreted from nearby matter. In such a binary star system, a strongly eccentric orbit produces strong gravitational forces on the circumstellar disks at periastron, and such disturbance can lead to a temporary increase in the accretion rate onto both stars. Simulations show that the accretion rate is likely to be highly symmetric between stars in nearly equal-mass binary systems but for systems with a mass disparity can be asymmetric. Such asymmetry may be attributable to a high eccentricity circumbinary disk which can accrete material onto the surface of one star at a rate 10-20 times greater than onto the other, with the star that experiences a higher rate of accretion alternating with its companion over large time scales.