Various amounts of carbon black (CB) and carbon nanofibres (CNF) were dispersed in an epoxy resin to prepare nanocomposites whose mechanical behaviour, under ramp and creep conditions, was monitored by electrical measurements. The electrical resistivity of the epoxy resin was dramatically reduced by both nanofillers after the percolation threshold (1 wt% for CB and 0.5 wt% for CNF), reaching values in the range of 10^3–10^4 Ohm cm for filler loadings higher than 2 wt%. Due to the synergistic effects between the nanofillers, an epoxy system containing a total nanofiller amount of 2 wt%, with a relative CB/CNF ratio of 90/10 was selected for the specific applications. A direct correlation between the tensile strain and the increase of the electrical resistance was observed over the whole experimental range, and also the final failure of the samples was clearly detected. Creep tests confirmed the possibility to monitor the various deformational stages under constant loads, with a strong dependency from the temperature and the applied stress. The obtained results are encouraging for a possible application of nanomodified epoxy resin as a matrix for the preparation of structural composites with sensing (i.e., damage-monitoring) capabilities.