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The influence of the normal material in a superconducting wire on the selffield losses has been investigated. The results show that the contribution of the normal material is considerable in the case of a highly conductive material like Cu. Measurements on wires with CuNi-material show no significant contribution of the normal material to the losses. In the latter case, however, special attention should be paid to stability. Measurements show that the obtainable maximum current under a.c. conditions obeys the adiabatic stability criterion rather well. The dependence of the maximum current amplitude on the critical current density and the diameter of the wire has been obtained. Wires with Al cores inside the NbTi filaments for better stabilization have also been investigated regarding maximum current and selffield losses.