Objective. Current retinal prosthetics are limited in their ability to precisely control firing patterns of functionally distinct retinal ganglion cell (RGC) types. The aim of this study was to characterise RGC responses to continuous, kilohertz-frequency-varying stimulation to assess its utility in controlling RGC activity. Approach. We used in vitro patch-clamp experiments to assess electrically-evoked ON and OFF RGC responses to frequency-varying pulse train sequences. In each sequence, the stimulation amplitude was kept constant while the stimulation frequency (0.5–10 kHz) was changed every 40 ms, in either a linearly increasing, linearly decreasing or randomised manner. The stimulation amplitude across sequences was increased from 10 to 300 µA. Main results. We found that continuous stimulation without rest periods caused complex and irreproducible stimulus-response relationships, primarily due to strong stimulus-induced response adaptation and influence of the preceding stimulus frequency on the response to a subsequent stimulus. In addition, ON and OFF populations showed different sensitivities to continuous, frequency-varying pulse trains, with OFF cells generally exhibiting more dependency on frequency changes within a sequence. Finally, the ability to maintain spiking behaviour to continuous stimulation in RGCs significantly reduced over longer stimulation durations irrespective of the frequency order. Significance. This study represents an important step in advancing and understanding the utility of continuous frequency modulation in controlling functionally distinct RGCs. Our results indicate that continuous, kHz-frequency-varying stimulation sequences provide very limited control of RGC firing patterns due to inter-dependency between adjacent frequencies and generally, different RGC types do not display different frequency preferences under such stimulation conditions. For future stimulation strategies using kHz frequencies, careful consideration must be given to design appropriate pauses in stimulation, stimulation frequency order and the length of continuous stimulation duration.