To account for the cessation of human life span increase in developed countries, we have studied the Swedish vital statistics over the period of 1901-1978. Approximating age-related mortality dynamics as the sum of the constant (age-independent mortality) and exponential (age-dependent mortality), we have discovered a striking phenomenon consisting in historical stability of age-dependent mortality. It appeared that decrease in total mortality was exclusively due to age-independent mortality which is close now to the limiting (zero) level. The results obtained prove the existence of the biological limit for the average life span and show that the conventional reserves for decrease in mortality have been exhausted. Thus, the problem of life prolongation requires a new way of thinking.