A review is given of the application of cyclic analytical methods in capillary electroseparation (CE) and liquid chromatography (LC) systems. Cyclic methods have been used since the early sixties in chromatographic systems to overcome pressure limitations to resolution. From the early nineties on they have also been applied in capillary electroseparation systems to overcome voltage limitations. Some basic theory is given, outlining the temporal development of resolution in cyclic CE and LC systems and calculating the maximal resolution that can be obtained as a function of the operational parameters of pressure and electrical field. Simple equations are given for the temporal change in the peak capacity and the loss of peaks from the systems as it occurs in some cyclic systems. Finally, a circular open tubular chromatographic system is proposed using integrated pumping and continuous detection. The performance of such a system is discussed using magnetohydrodynamic and alternating current electroosmotic pumping as examples of integrated pumps and Shah Convolution Fourier transform detection as an example of a continuous detection method.