Cross-sectional analyses show that an index of aging-associated health/well-being deficits, called the "frailty index", can characterize the aging process in humans. This study provides support for such characterization from a longitudinal analysis of the frailty index properties. The data are from the National Long Term Care Survey assessed longitudinally health and functioning of the U.S. elderly in the period 1982-1999. In cross-sectional analysis, the frailty index exhibits accelerated increase with age till oldest-old ages (95+), with possible deceleration thereafter. Longitudinal analysis confirms the accelerated accumulation of deficits in aging individuals. The time-dynamics of the frailty index is affected by two sex-sensitive processes: (i) selection of robust individuals, resulting in a decline of the mean frailty index with age and (ii) accumulation of deficits associated with physiological aging and its interaction with environment, which results in an accelerated increase of individual frailty index prior to death irrespective of chronological age. Current frailty index levels in individuals are more predictive of death than the index past values. Longitudinal analysis provides strong evidence that the cumulative index of health/well-being deficits can characterize aging-associated processes in humans and predict death better than chronological age during short-term periods.