An experimental study of flow transition in a rotating Taylor–Couette system was made by investigating the spatio–temporal velocity field (axial velocity component) by the ultrasonic Doppler method. The flow fields for the range of Reynolds numbers 9<R*<40 (where R*=R/Rc; Rc is the critical Reynolds number for Taylor vortex flow) were decomposed by two-dimensional Fourier transform and the orthogonal decomposition technique, and intensities of coherent structural modes were quantitatively obtained. The variation of the intensities of various modes with respect to Reynolds number clearly shows a transition behaviour of the quasi-periodic state resulting from the wavy vortex mode and the modulating waves, which is found to disappear suddenly at about R*=21. A new mode was found after the disappearance of the quasi-periodic state, which in turn disappears at R*=36. Beyond this regime, there was no coherent structure found except for the stationary Taylor vortices and so-called broad-band component, which is attributed to chaos. The total energy occupation (the number of modes which occupy 90% of the total energy) and the global entropy support such transition behaviour quantitatively. After the disappearance of the newly found mode, the number of modes needed to compose the velocity field is still finite and small – about 40–50. We call this flow state ‘soft turbulence’.