The electrical properties of segments of tapered InAs nanowires (NWs) were investigated by in situ transmission electron microscopy with simultaneous I-V measurements using good ohmic contacts, thus excluding experimental artefacts as Joule heating caused by high-resistivity contacts. At low voltage the resistivity of InAs NWs with a diameter larger than 120 nm is constant (similar to 10(-2) Omega center dot cm). When the current is strongly increased a breakdown of the NW occurs close to the cathode side, whereby the main changes are an electromigration of In and a sublimation of As. The critical current density for breakdown was close to 10(6) A cm(-2) in most cases. A Joule heating and electromigration mechanism for the breakdown process is proposed.