Superconducting wires with a CuNi matrix for a.c. applications are not fully stabilized and normal transition is easily induced by various disturbances because the CuNi matrix has a high electrical resistivity and a very low thermal conductivity. We have investigated normal-zone propagation velocities in NbTi/CuNi superconducting wires[l]. In a.c. applications of superconductivity we also need to know the thermal and the electromagnetic behaviour during such the abrupt increase of currents as short-circuit current in superconducting transformers, the current changing in superconducting current limiters and the current redistribution during quench process in multi-strand cables. We measured the degradation of the quench current of NbTi superconducting wires with a CuNi matrix as a function of the current sweep rate in the range of 10 A/s to 100 kA/s and the initial current, which is a transport current-just before current changing. Experimental data is compared with analytical results by the finite element method taking the magnetic and the thermal diffusion in radial direction of wire cross-section into account. From these comparisons, the relation between the rate of current changing and the degradation of the quench current in superconducting wires is discussed.