The initial stages of the interaction of daunomycin (DNM) with drug‐sensitive (P388/S) and drug‐resistant (P388/100) cells have been defined by a rapid kinetics stopped‐flow procedure. The process can be described by two kinetic components. The faster component accounts for rapid occupation of cell surface sites by DNM, as supported by experiments with liposomes with different surface charge. On the other hand, the effect of verapamil in the assays, suggests that the slower component is involved in the transport of the drug into the cells. Our observations are consistent with a loss in the control of the passive permeability to the drugs in the drug‐resistant tumor cells.