An estimator for the load share parameters in an equal load-share model is derived based on observing k-component parallel systems of identical components that have a continuous distribution function F (.) and failure rate r(.). In an equal load share model, after the first of k components fails, failure rates for the remaining components change from r(t) to gamma(1)r(t), then to gamma(2)r(t) after the next failure, and so on. On the basis of observations on n independent and identical systems, a semiparametric estimator of the component baseline cumulative hazard function R = - log(1 - F) is presented, and its asymptotic limit process is established to be a Gaussian process. The effect of estimation of the load-share parameters is considered in the derivation of the limiting process. Potential applications can be found in diverse areas, including materials testing, software reliability and power plant safety assessment.