In this paper we consider a competition model between plasmid-bearing and plasmid-free organisms in a chemostat that incorporates both general response functions, distinct yields and distinct removal rates. The model with identical removal rates and identical yields was studied in the existing literature. The object of this paper is to provide the local analysis of the model in the case of dierent removal rates and distinct yields. In this case the conservation law fails. The operating diagram giving the asymptotic behaviour of the model with respect of the operating parameters is also presented.