Получено описание некоторого класса экспоненциальных мономов на локально компактных абелевых группах.We describe the structure of some class of exponential monomials onsome locally compact abelian groups. The main result of the paper is the next theorem.Let G* and G be locally compact abelian groups, a : G* -> G be acontinuous surjective homomorphism and H be a kernel of a. If a is aan open maps from G* to G then any exponential monomial Ф(t) on thegroup G*, which satisfy the condition Ф(t + h) = Ф(t) for all h in H; t in G* can be presented in the form Ф(t) = f(a(t)) for some exponential monomial f(x) on the group G.