A method of and apparatus for tuning an AFT-controlled channel selecting apparatus of the type having a storage device for storing digital representations corresponding to predetermined channel frequencies from which a selected representation is read out and converted to a control voltage which is applied to a controllable tuning element included in an electronic tuner. When the control voltage is applied, generally it experiences a gradual increase in magnitude until its predetermined control voltage level is attained. The automatic fine tuning (AFT) circuit may pull in a frequency corresponding to the instantaneous level of the control voltage during the gradual increase in magnitude thereof. To avoid tuning the electronic tuner to such an unwanted pulled-in frequency, the AFT operation is carried out at a relatively slow rate when the tuning of the tuner approaches the frequency corresponding to the read out representation and then at a relatively fast rate when the tuner is tuned to a frequency that deviates from the desired frequency within a predetermined range.