Abstract. The preparation process of two recent earthquakes (EQs) that occurred in Cephalonia (Kefalonia), Greece, ((38.22 • N, 20.53 • E), 26 January 2014, M w = 6.0, depth ∼ 20 km) and ((38.25 • N, 20.39 • E), 3 February 2014, M w = 5.9, depth ∼ 10 km), respectively, is studied in terms of the critical dynamics revealed in observables of the involved non-linear processes. Specifically, we show, by means of the method of critical fluctuations (MCF), that signatures of critical, as well as tricritical, dynamics were embedded in the fracture-induced electromagnetic emissions (EMEs) recorded by two stations in locations near the epicentres of these two EQs. It is worth noting that both the MHz EMEs recorded by the telemetric stations on the island of Cephalonia and the neighbouring island of Zante (Zakynthos) reached a simultaneously critical condition a few days before the occurrence of each earthquake. The critical characteristics embedded in the EME signals were further verified using the natural time (NT) method. Moreover, we show, in terms of the NT method, that the foreshock seismic activity also presented critical characteristics before each event. Importantly, the revealed critical process seems to be focused on the area corresponding to the western Cephalonia zone, following the seismotectonic and hazard zoning of the Ionian Islands area near Cephalonia.