In this paper, the problem of state estimation of a bioreactor containing a single substrate and several competing species is studied. This scenario is well-known as the competition model, in which multiple species compete for a single limiting nutrient. Considering the total biomass to be the only available measurement, the challenge is to estimate the concentration of the whole state vector. To achieve this goal, the estimation scheme is built by the coupling of two estimation techniques: an asymptotic observer, which depends solely on the operating conditions of the bioreactor, and a finite-time parameter estimation technique, which drops the usual requirement of the persistence of excitation. The presented methodology achieves the estimation of each competing species and a numerical example illustrates the intended application.