A one-component epoxy-modified polyurethane and/or urea adhesive comprising in admixture: at least one of components A and B, wherein component A) is one or more non-rubber-modified epoxy resins and component B) is one or more rubber-modified epoxy resins; C) one or more reactive urethane group- and/or urea group-containing tougheners having a number average molecular weight of up to 35,000, at least one polyether or diene rubber segment having a weight of at least 1000 atomic mass units, and capped isocyanate groups of which at least 75% are monophenol- or polyphenol-capped isocyanate groups; D) optionally, one or more core-shell rubbers; E) one or more latent epoxy curing agents; and F) at least one catalyst for the reaction of an epoxide with the curing agent(s); wherein 1) component A constitutes 0 to 40 percent of the combined weight of components A-E; 2) component B constitutes 0 to 40 percent of the combined weight of components A-E; 3) components A and B together constitute 12 to 40 percent of the combined weight of components A-E; 4) component C constitutes 55 to 85 percent of the combined weight of components A-E; 5) components B, C and D together constitute 65 to 97 percent of the combined weight of components A-E; 6) component D constitutes 0 to 15 percent of the combined weight of components A-E; and 7) components A-E together constitute at least 60 weight percent of the one-component epoxy adhesive. at least one of components A and B, wherein component A) is one or more non-rubber-modified epoxy resins and component B) is one or more rubber-modified epoxy resins; C) one or more reactive urethane group- and/or urea group-containing tougheners having a number average molecular weight of up to 35,000, at least one polyether or diene rubber segment having a weight of at least 1000 atomic mass units, and capped isocyanate groups of which at least 75% are monophenol- or polyphenol-capped isocyanate groups; D) optionally, one or more core-shell rubbers; E) one or more latent epoxy curing agents; and F) at least one catalyst for the reaction of an epoxide with the curing agent(s); wherein 1) component A constitutes 0 to 40 percent of the combined weight of components A-E; 2) component B constitutes 0 to 40 percent of the combined weight of components A-E; 3) components A and B together constitute 12 to 40 percent of the combined weight of components A-E; 4) component C constitutes 55 to 85 percent of the combined weight of components A-E; 5) components B, C and D together constitute 65 to 97 percent of the combined weight of components A-E; 6) component D constitutes 0 to 15 percent of the combined weight of components A-E; and 7) components A-E together constitute at least 60 weight percent of the one-component epoxy adhesive. 1) component A constitutes 0 to 40 percent of the combined weight of components A-E; 2) component B constitutes 0 to 40 percent of the combined weight of components A-E; 3) components A and B together constitute 12 to 40 percent of the combined weight of components A-E; 4) component C constitutes 55 to 85 percent of the combined weight of components A-E; 5) components B, C and D together constitute 65 to 97 percent of the combined weight of components A-E; 6) component D constitutes 0 to 15 percent of the combined weight of components A-E; and 7) components A-E together constitute at least 60 weight percent of the one-component epoxy adhesive.