The invention relates to polyaldimines which may be obtained from at least one polyamine (A) with aliphatic primary amino groups and at least one aldehyde (B). Said polyaldimines are odorless as are the aldehydes (B) produced by hydrolysis thereof. The invention further relates to methods for production of said polyaldimines and aldehyde (B) and methods for hydrolysis of the polyaldimine. The use of said polyaldimine in compositions as adhesive, sealant, coating or covering agents is disclosed. Said polyaldimines are characterized in being odorless, rapidly hydrolyzed on contact with water, no detectable odors being generated after hydrolysis thereof and stable to storage with the exclusion of water in compositions which contain components reactive towards amines.