Аннотация
In the article a method of reducing a linear system with a differentiation operator in the direction of the main diagonal to a canonical form is proposed. It is assumed that the condition of reducibility of this linear system to a higher order one equation is not fulfilled. This leads to cases when the system fall into independent linear systems and supsystems of stepped form. On the basis of the results obtained, it is possible to find out the structure of the solutions and investigate the conditions of the existence and uniqueness of the multiperiodic solution of the linear $$D_{e}$$ -system of equations.