Transient photoconductivity in nominally undoped (n-type background doping) Ga0.47In0.53As/InP multiquantum well heterostructures is reported. The observed responses exhibited an initial fast decay followed by a much slower subsequent decay. The slow decay was consistent with a kinetic radiative recombination model which included free carriers, excitons and photon recycling. A model describing the fast initial decay is presented in terms of fast barrier radiative recombination. A comparison between the experimental results and the model shows good agreement.