Recent observational and theoretical studies have raised the possibility that the collimated outflows in gamma-ray burst (GRB) sources have two distinct components: a narrow (opening half-angle θj,n), highly relativistic (initial Lorentz factor ηn ≳, 102) outflow, from which the gamma-ray emission originates, and a wider (θj,w ≲ 3θj,n), moderately relativistic (ηw ∼ 10) surrounding flow. Using a simple synchrotron emission model, we calculate the R-band afterglow light curves expected in this scenario and derive algebraic expressions for the flux ratios of the emission from the two jet components at the main transition times in the light curve. For viewing angles θobs < θj,n we find that the contribution of the wide component to the optical afterglow is negligible if its kinetic energy Ew is significantly smaller than that of the narrow component, En, as expected for the jet core and cocoon outflow components in the collapsar jet breakout model. However, if E w/En > 1 [but the isotropic equivalent energy ratio Eiso,w/Eiso,n = (Ew/En) (θj,n/θj,w)2 remains <1], as expected for the decoupled neutron (wide) and proton (narrow) components in an initially neutron-rich, hydromagnetically accelerated jet model, then the narrow component only dominates the early afterglow and the wide component takes over after its nominal deceleration time tdec,w (typically ∼0.1-1 days). Given that tdec,w is comparable to the jet break time t jet,n of the narrow component for characteristic parameter values, the emergence of the wide component at tdec,w may mask the jet break in the narrow component at tjet,n, which in turn may lead to an overestimate of the gamma-ray energy emitted by the source and hence of the required gamma-ray emission efficiency. We apply this scheme also to X-ray flash sources, which we interpret as GRB jets viewed at an angle θ obs > θj,n. Finally, we argue that a neutron-rich hydromagnetic outflow may naturally give rise to repeated brightening episodes in the afterglow light curve as observed in GRB 021004 and GRB 030329.