Assuming that the distribution of individuals and the competition mode of individuals are for the same resource, interspecific competition models dependent on distribution of individuals are established in a bottom-up manner for two species in a habitat according to the site-based framework model. The assumed distribution of individuals has three types, i.e. Poisson distribution, the negative trinomial distribution and the independent negative binomial distribution. The assumed competition model of individuals in the same resource has three kinds, i.e. scramble competition, contest competition and intermediate competition. According to the combination of competition models of the two species and the distribution of individuals, various interspecific competition models can be derived. In this paper, two different interspecific competition models with the negative trinomial distribution are established, within which the competition modes are of scramble vs. contest and scramble vs. intermediate competition s respectively.