The low temperature non-exponential transients of photoconductivity build-up in gallium doped Cd0.99Mn0.01Te and CdTe alloys possessing DX centers were studied. It was found that the two-exponential model commonly used to explain the persistent photoconductivity growth in semiconductors with DX centers describes properly solely the photokinetics obtained for CdTe:Ga. In the case of Cd 0.99 Mn 0.01 Te:Ga the stretched-exponential approach is more appropriate, for it explains the short-time power-law exhibited by the experimental data.