Downconversion of one visible photon into two infrared photons has been reported for the lanthanide ion couple ( Pr3+ , Yb3+ ) in a variety of host lattices. The mechanism responsible for downconversion is controversial and has been reported to be either a two-step energy transfer process (via two first-order transfer steps, the first being cross relaxation) or cooperative energy transfer from Pr3+ to two Yb3+ ions (a second-order process). Here we report experiments on downconversion for the ( Pr3+ , Yb3+ ) in LiYF4 . Luminescence decay curves of the Pr3+ emission are recorded as a function of the Yb3+ concentration and analyzed using Monte Carlo simulations for both cooperative energy transfer and energy transfer through cross relaxation. We obtain a good agreement between experiment and simulations for energy transfer by cross relaxation but not for cooperative energy transfer. The observation that cross relaxation is more efficient than cooperative energy transfer is consistent with Judd-Ofelt calculations for the transition probabilities involved in the two energy transfer processes and the lower probability for the second-order cooperative transfer