Abstract We have investigated hot-drawn PbMo 6S 8 composite monofilament wires ( J c = 4.6 x10 8 A/ m 2 at μ 0 H = 10 T and T = 4.2 K) in particular steps that occur in the I-U transition curves. These steps have been measured in fields up to 9 T and in a temperature range between 2 K and 10 K. We have analyzed them by considering two models, the hot spot model and the phase-slip model. Furthermore, a flux flow channel picture is developed, where the step is related to an avalanche of flux flow localised in a narrow channel. The observed field dependence of the step in a field applied transversally to the wire can be understood within this description. All these model considerations concur; the origin of the steps appears to lie in local defects with a μm length-scale. Just a few of these defects may already depress the overall critical current in a substantial way. Taking into account this situation, there exists an important potential for further improvements of the critical current in PbMo 6S 8 wires.