The related problems on bihypergenic functions are considered in this paper. First, the Plemelj formula of the bihypergenic quasi-Cauchy type integral is given. Then, using the compression mapping principle the existence and uniqueness of the solution to the linear boundary value problem $LB$ are proved and the boundary value problem $NB$ is solved using Schauder fixed point theorem. Finally, that the composition of a bihypergenic function with a Clifford M$\ddot{o}$bius transformation under certain conditions leads to a bihypergenic function is proved.