‎This paper will analyze inflated bivariate mixed count data‎. ‎The estimations of model parameters are obtained by the maximum likelihood method‎. ‎For a bivariate case which has inflation in one or two points‎, ‎the new bivariate inflated power series distributions are presented‎. ‎These inflated distributions are used in joint modeling of bivariate count responses‎. ‎Also‎, ‎to illustrate the utility of the proposed models‎, ‎some simulation studies are performed‎. ‎and finally‎, ‎a real dataset is analyzed‎.