Limits to the total mass-loss in red giants in globular clusters are calculated on the basis of Sweigart and Gross (1976) Horizontal Branch models by means of Sweigart and Gross (1978) Red Giant Branch stellar models. The upper limit is obtained through the condition that the stars do not leave their nuclei bare. The lower limit results from the requirement that, when reaching the Zero Age Horizontal Branch, they do not exceed the giant branch to the right. Both limits are calculated for several values of the metal and helium contents and age of the galactic globular cluster system. Mass-loss rates are also estimated using the Sweigart and Gross (1978) life times of red giants; the results obtained are in the range 0 < dM/dt < 6×10-8M_sun;yr-1. From the present results it ensues that, for fixed chemical composition, older systems are associated with lower total mass-loss. The helium content is also inversely related to the total mass-loss. Finally, the opposite applies for the metallicity of the clusters: higher metal content is positively correlated with higher total mass-loss and higher mass-loss rates.