Using Deep Level Transient Spectroscopy (DLTS), we have investigated the properties of the DX center in GaAsP for the whole range of alloy composition x. We have determined the variation of the defect characteristics (thermal ionization energy Ei, barrier for electron capture B, and energy level location EDX) versus x. From the relationship that exists between Ei, B and EDX, and between B and Δ, the energy difference between the L band and the bottom of the conduction band, we deduce that electron emission and capture occur from and to the DX center via the L band in the same fashion as in GaAlAs alloys. A good fit of the variation of Ei and B versus x is obtained in a model where the DX level is a donor state associated with the L band which is 200 meV deep, like in GaAlAs, as a result of intervalley mixing.