We have investigated the kinetics of interaction of cationic fluorescent lipophiles (dyes) rhodamine 123, rhodamine 6G, tetramethyl rhodamine ethyl ester, safranine O, 1,1'-diethyloxacarbocyanine, 1,1'-diethyloxadicarbocyanine, and 1,1'-diethylthiadicarbocyanine iodide with isolated respiring rat-liver mitochondria (RLM). Dye flux across the RLM inner membrane was measured by following the kinetics of fluorescence signal change after mixing of dye and RLM. The time course of fluorescence was analysed in terms of a kinetic model of the binding and transport processes involved. The rate constants of dye influx and efflux were extracted from the observed effect on the apparent time constant of fluorescence change to equilibrium intensity upon mixing dye with increasing concentrations of RLM. From the influx rate constants obtained, the apparent permeability constants for dye influx (at zero potential) across the membrane were calculated and ranged from 3 to 140 x 10(-4) cm/s. The influx rate constant was found to be linearly related to relative dye lipophilicity, as predicted by the model. As another test of the model, from the ratio of the influx and efflux rate constants, the apparent trans-membrane potential, psi, was calculated and found generally to agree with reported values, but to depend on the lipophilicity of the dye used. Not predicted by the simple model was a dissymmtry observed in the influx and efflux time constants for fluorescence change to equilibrium intensity. Inferences are made relating to the utility of these dyes as probes of psi.