A theory of the direct creation of excitonic molecule (biexciton) by direct two-photon absorption in semiconductor quantum well structures is developed. Analytical expression of the biexciton two-photon absorption coefficient is given for both photon polarizations. Excitonic-interband-two-photon and exciton one-photon processes in Quantum Wells (QW) have also been investigated. The analytical forms and numerical values of the momentum matrix elements involved in each process are provided. The biexciton matrix element has been calculated adopting a six-parameter variational wave function. A numerical estimation for GaAs QW shows that the biexciton two photon absorption (BTPA) process dominates the other processes by different orders of magnitude. This enhancement essentially comes from the resonance effect and the structure of the matrix elements included in each process. Furthermore, the (BTPA) process in QW for both polarizations is enhanced over its bulk value by about 4 and 5 orders of magnitude respectively. This increase is interpreted as due to the spatial confinement of the QW. (author). 16 refs, 4 tabs.