Epoxy adhesives include a latent curing agent, a reactive toughener having capped isocyanate groups, and certain urea compounds. The toughener is made by chain extending and capping a mixture of isocyanate-terminated prepolymers. The prepolymers include an isocyanate-terminated polyether and an isocyanate-terminated diene polymer. The adhesives have excellent wash-off resistance and excellent ability to adhere to oily substrates.