The intention is to provide an adhesive system which is stable in storage and which when used permits precise positioning of the adhesive, and which can be crosslinked without exceeding moderate temperatures. The said system is moreover intended to provide strong adhesive bonds that attain high performance levels. This is achieved via a kit containing at least two pressure-sensitive adhesive layers A and B, where the two pressure-sensitive adhesive layers A and B mutually independently respectively comprise at least one polymer containing a multiplicity of carboxy groups; in the pressure-sensitive adhesive layer A a portion of the carboxy groups of the polymer containing these has been activated by reaction with an activator AA; and—the pressure-sensitive adhesive layer A—at least one crosslinking agent VA which can enter into a crosslinking reaction with the carboxy groups of the polymer containing these of the pressure-sensitive adhesive layers A and B, but which in the pressure-sensitive adhesive layer A is not significantly reactive; —the pressure-sensitive adhesive layer B—at least one crosslinking agent VB which can accelerate the crosslinking reaction of the carboxy groups of the polymer containing these of the pressure-sensitive adhesive layer B with the crosslinking agent VA and which can permit and accelerate the crosslinking reaction of the carboxy groups of the polymer containing these of the pressure-sensitive adhesive layer A with the crosslinking agent VA and can enter into a crosslinking reaction with the activated carboxy groups of the polymer containing these of the pressure-sensitive adhesive layer A. The invention moreover also relates to an adhesive tape which is obtainable via contact between the pressure-sensitive adhesive layers of the kit, and to a process for producing said adhesive tape.