In this paper we consider two types of competitive relationships: interference and operational competition. Mathematical models of Volterra competition describe the case of interference competition. For the case of operational competition, alternative mathematical models are constructed, the analysis of stationary points for stability is carried out. The developed mathematical models of operational competition confirm the theory of neutrality, which actually denies competition as rivalry. Also, these models prove the simultaneous coexistence of biological populations in the case of renewable and non-renewable trophic resource.