The paper deals with the problems of the control system stability. The analysis of the stability of a system of the linear differential equations of the given form is conducted. Eight theorems and eight lemmas, which determine the conditions for the equation system stability, are proved. An infirm of the phase velocity on a class of stable quasipolynomials of the delay type is found. Stability criteria of the families of quasipolynomials are obtained on this basis. Classes of quasipolynomials preset by convex polyhedrons in the space of the coefficients, whose stability follows from the stability of quasipolynomials corresponding to vertices, are separated.