A new type of migrating zone boundary in electrophoresis is presented theoretically and evidenced experimentally. This type of the boundary (called hybrid boundary) shows simultaneously a steady-state part with self-sharpening properties and an unsteady-state part with time-dependent electromigration dispersion. It is shown that a sample zone may possess a hybrid boundary both as its front and rear one simultaneously. In such a case, the evolution of a sample zone injected originally as a rectangular pulse exhibits very complex transient shapes before it reaches the well-known fronting or tailing triangular shape. Depending on the stage at which detection of such a sample zone occurs, variable and peculiar-shape peaks may appear in the electropherogram. Based on theoretical predictions, experimental examples of the above-mentioned phenomena are presented in this contribution for direct and indirect UV absorbance detection of sample zones. Excellent agreement of theoretical predictions with the experiments has been found. The knowledge of hybrid boundaries is of key significance for correct interpretation of records of CE analyses in practice.