The instability of Taylor vortex flows in a gap with a small aspect ratio of concentric rotating cylinders has been investigated. For both the asymmetric and symmetric end conditions, the critical Reynolds number of the transition from the Taylor vortex flow to the wavy Taylor vortex flow has been revealed. In the asymmetric case, the bifurcations between odd numbers of cells and between an odd number and even number of cells are shown in relation to the aspect ratio and Reynolds number. In addition, the bifurcation diagram is drawn in the neighborhood of a certain aspect ratio. The relations, as priority, between primary flow and secondary flow on a bifurcation set are discussed.