A stage-class population model with density-feedback term included was used to identify the most critical parameters determining the population dynamics of female Spanish ibex (Capra pyrenaica) in southern Spain. A population in the Cazorla and Segura mountains is rapidly declining, but the eastern Sierra Nevada population is growing. The stable population density obtained using estimated values of kid and adult survival (0.49 and 0.87, respectively) and with fecundity equal to 0.367 in the absence of density feedback is 12.7 or 16.82 individuals/km², based on a non-time-lagged and a time-lagged model, respectively. Given the maximum estimate of fecundity and an adult survival rate of 0.87, a kid survival rate of at least 0.41 is required to avoid extinction. At the minimum fecundity estimate, kid survival would have to exceed 0.52. Elasticities were used to estimate the influence of variation in life-cycle parameters on the intrinsic rate of increase. Adult survival is the most critical parameter, while fecundity and juvenile survival are less important. An increase in adult survival from 0.87 to 0.91 in the Cazorla and Segura mountains population would almost stabilize the population in the absence of stochastic variation, while the same increase in the Sierra Nevada population would yield population growth of 4–5% per annum. A reduction in adult survival to 0.83 results in population decline in both cases.