We present an extensive study of lithium abundances in dwarf components of chromospherically active binary stars (CABS). Since most of these binaries have known radii, masses and ages, this kind of data is especially useful for comparisons with theoretical models which try to explain the Li depletion phenomenon. We show that a significant part of these stars have clear Li overabundances with respect to the typical values for stars of the same mass and evolutionary stage. These excesses are evident when comparing our sample of CABS with binary and single stars belonging to open clusters of different ages, namely Pleiades, Hyades, NGC 752, M 67 and NGC 188, which have ages ranging from 7x10^7^ to 10^10^yr. The Li excesses are more conspicuous for masses in the range 0.75-0.95Msun_, indicating that the rate of Li depletion has been less pronounced in CABS than in single stars. This phenomenon is interpreted in the context of transport of angular momentum from the orbit to the stellar rotation due to tidal effects. This angular momentum transfer would avoid the radial differential rotation and the associated turbulent mixing of material in the stellar interior. Other explanations, however, can not be ruled out. This is the case of transport of material induced by internal gravity waves, which could be inhibited due to the presence of strong magnetic fields associated with the effective dynamo in CABS. The confirmed existence of a relation between Li abundances and the fluxes in CaII H&K lines can also be accommodated within both scenarios.