Hot-curing structural adhesives with multiphase polymer morphology, wherein the binder matrix of the cured chemically reactive adhesive displays (a) a continuous phase containing a polymer P1 having a glass transition temperature of over 100° C.; (b) a heterodisperse phase consisting of individual continuous domains of a thermoplastic or elastomeric polymer P2 having a glass transition temperature of below −30° C. and an average particle size of between 0.5 and 50 μm, which itself contains separate phases of another thermoplastic or elastomeric polymer P3 having a glass transition temperature of below −30° C. and a size of between 1 nm and 100 nm, parts of which can be in aggregated form as larger agglomerates; and (c) another heterodisperse phase embedded in the continuous phase and consisting of domains of the polymer P3, at least parts of which have an average particle size of between 1 nm and 50 nm, wherein P3 is not identical to P2; are suitable as high-strength, impact resistant structural adhesives, for internal stiffeners for cavities in automobile construction and for the production of reinforcing coatings for thin-wall sheet components.