We show that the two-dimensional quantum confined Stark effect in a semiconductor quantum wire can display novel behaviour, i.e. wave function splitting and cascading. No analog to these phenomena can be found in bulk material or quantum wells. The consequences of these effects on Stark shifts, oscillator strengths and electroabsorption spectra are explored numerically using k.p theory. A non-trivial prediction of our model is that, for the case of hole wave function splitting, the cascading of the ladder of states gives rise to observable duplications of the lowest peaks in the interband absorption spectra.