We consider the propagation of acoustic waves in an ocean sound channelC(z, x) with slow dependence onx. The travel timetRDin the range-dependent channel differs from the travel timetRAthrough the range-averaged sound channelCRA(z) = ±C(z, x)⟩x. The Hamiltonian formulation (Wunsch, in press) takes advan tage of the nearly periodic (inx) paths of the ray loops. The biastRD-tRAfor anadiabatic x-dependence is a function only of the variance in the channel parameters. Generally (but not always)tRD<tRA, thus giving a “warm bias” in the range-averaged ocean for any inversion of the acoustic travel times which ignores the range dependence of the sound channel. We derive bias formulae for three models ofx-dependence, corresponding to perturbations of the first and second baroclinic modes, respectively, and to anx-dependent surface warming.