Short-circuit peak currents exceeding the testing value according IEC standards can be caused by the nonsimultaneous closing of the poles of a circuit breaker during switching or reclosing while the network is in short-circuit state and by the successive involvement of the three phases during the development of a three-phase fault as well. The paper treats the theoretical relations of the short-circuit currents during non-simultaneous pole closing or fault development in a network where either the source or the fault is ungrounded. In a network satisfying the IEC test circuit the peak current may reach a value up to 2.1 p.u., this is well above the maximum prospective value of 1.8 p.u. achieved during testing with simultaneous closing of the three phases. The chance of peak currents occurring above 1.8 p.u. have been investigated by TNA (transient network analyser) tests. Parameters are the dispersion in the closing times of the CB poles and the prestrike characteristics of the breaker. The tests indicate that these chances are quite high in modern circuit breakers. The paper also considers the resulting short-circuit current when a short-circuit happens during the energisation of a capacitor bank. In this situation, the chance of peak currents occurring well above 1.8 p.u. is rather small as the required coincidence of conditions is less probable.