The kinetics of ligand equilibration between the tubular and vesicular parts of the endosome are studied for ligands diffusing in the vesicle and in a narrow cylindrical tubule attached to it. The key quantity in our analysis is the fraction of ligands in the vesicle at time t, P(ves)(t). We derive an expression for the Laplace transform of P(ves)(t) as a function of the vesicle volume and the length and radius of the tubule as well as the ligand diffusion coefficients in the vesicle and in the tubule. This transform is used to find the average equilibration time as a function of the system parameters.