A process for preparing high molecular weight acyclic polyamines comprising providing a reaction mixture that includes at least a first component comprising a first organic, nitrogen-containing compound that contains at least two non-tertiary amine groups separated from one another by a ternary or higher carbon atom spacing that can be transaminated in the presence of a hydrogenation/dehydrogenation catalyst to form a mixture of higher molecular weight, acyclic polyamines while minimizing the formation of cyclic polyamines.