Abstract: The classical Lotka-Volterra competition equations are the direct extension of the classical Logistic equation of single population growth. Because they have no necessary theoretical basis and oversimplify the process of interspecific competition, it is not suitable for Lotka Volterra competition equations to be a general theoretical model of interspecific competition. Based upon the theory of nutrition kinetics, a new kind of competition model is constructed as follows: dX₁/dt=μ_c1*X₁ * 1-(X₁+a₁₂X₂)/X_m1^*/1-(X₁+a₁₂X₂)/X_m1^′ dX₂/dt=μ_c2*X₂ * 1-(X₂+a₂₁X₁)/X_m2^*/1-(X₂+a₂₁X₁)/X_m2^′ They are the extension of Cui-Lawson model of single population growth which is as follows: dX/dt=μ_c^*X * 1-X/X_m^*/1-X/X_m^′ The new competition model has more complex and extensive behaviours than Lotka Volterra competition equations, and under specific condition, it turns into Lotka-Volterra competition equations. Therefore, the new competition equations are more general, and are the expansion of classical Lotka-Volterra competition equations.

Key words: Modelling, Nutrition kinetics, Competition, Lotka-Volterra equations, Functional response