A profile assembly having a first profile and having a second profile connected on its long side to the first profile, which two profiles each have a hook strip integrally formed on the long side, wherein the hook projection of the hook strip of the first profile points in the one direction, and the hook projection of the hook strip of the second profile points in the opposite direction, the hook strips brought into engagement with one another in a claw-like manner. The first profile has an anchoring channel following its longitudinal extent, and the hook strip of the second profile has a clamping strip which is integrally formed thereon, which hook strip is secured by its hook projection and its clamping strip in the anchoring channel of the other profile by a cold joining connection. In order to produce the cold joining connection, one of the two hook strips comprises an adjusting strip which is formed by the cold joining process and which is supported in the produced profile assembly by its free end face while being under prestress. The hook strip secured in the anchoring channel is placed under prestress within the anchoring channel, at two points situated opposite one another in the direction of the height of the profile assembly, with respect to the adjoining portions of the first profile as a result of the cold joining connection.