A flexible, electrically-conductive, one-component epoxy adhesive composition and method for making the same are provided. The present adhesive composition comprises: (a) at least one polyepoxide resin having a hardness not exceeding a durometer Shore D reading of about 45 when cured with a stoichiometric amount of diethylene triamine; (b) a substantially stoichiometric amount of curing agent including at least one amine-terminated butadiene-acrylonitrile polymer; and (c) an electrically-conductive filler. The epoxy adhesive, upon cure, has a volume resistivity not exceeding about 10.sup.-3 ohm-cm at room temperature and a drop resistance such that a 6-mil-thick (0.015 cm) bond effected by the adhesive can withstand at least six 60-inch (152 cm) drops onto a hard surface. Optional components in the epoxy adhesive include secondary rigid and semi-rigid epoxy resins, secondary amine curing agents, non-reactive flexibilizers, diluents, and processing aids. The adhesive bonds achieved using these epoxy adhesives are non-brittle, flexible, resilient, and drop-resistant, while also exhibiting strong adhesion and good processing characteristics.