In the paper we consider systems of linear autonomous functional differential equations (FDEs) of delayed type, the coefficients in a system can be of any sign. These FDE systems include equations with various types of aftereffects, including concentrated and distributed delays.The purpose of this paper is to obtain new effective conditions of stability for systems of linear autonomous FDEs. The study is based on an idea of constructing a so-called “comparison system”, which, on the one hand, has a simpler structure, and on the other hand, the same asymptotic properties as the original system. The comparison system may contain a delay, and not only concentrated, but also distributed. The comparison system is constructed in such a way that all components of its fundamental matrix are non-negative. Since the coefficient matrices in the comparison system are diagonal, it can be considered as a set of independent scalar equations. For the fundamental solutions of such equations in the papers of V.V. Malygina and K.M. Chudinov, exact two-sided exponential estimates were obtained, which also give an exponential estimate for the fundamental matrix of the comparison system.For autonomous FDEs of a delayed type, as is known, approaching zero always occurs exponentially, which means the existence of such positive constants N and α that . However, without specifying estimates for the coefficient N and exponent α or an algorithm for their effective calculation, the exponential stability problem cannot be considered completely solved. In the article, along with new conditions of stability, estimates of the rate at which solutions approach zero are found. The effectiveness of the results obtained is illustrated by several examples in which FDEs with different types of aftereffects are selected as comparison systems.

systems of functional differential equations, exponential stability, fundamental matrix, solution rate estimate, monotone operators.