The reaction A+B -->B is studied when the reactants diffuse in phase space, i.e., their dynamics is described by the Langevin equation. The steady-state rate constants are calculated for both the target (static A and mobile B's) and trapping (mobile A and static B's) problems when the reaction is assumed to occur at the first contact. For Brownian dynamics (i.e., ordinary diffusion), the rate constant for both problems is a monotonically decreasing function of the friction coefficient gamma. For Langevin dynamics, however, we find that the steady-state rate constant exhibits a turnover behavior as a function of gamma for the trapping problem but not for the target problem. This turnover is different from the familiar Kramers turnover of the rate constant for escape from a deep potential well because the reaction considered here is an activationless process. (C) 2001 American Institute of Physics.