  We study the stability of general $n$-dimensional nonautonomous linear
differential equations with infinite delays. Delay independent criteria, as
well as criteria depending on the size of some finite delays are established.
In the first situation, the effect of the delays is dominated by non-delayed
diagonal negative feedback terms, and sufficient conditions for both the
asymptotic and the exponential asymptotic stability of the system are given. In
the second case, the stability depends on the size of some bounded diagonal
delays and coefficients, although terms with unbounded delay may co-exist. Our
results encompass DDEs with discrete and distributed delays, and enhance some
recent achievements in the literature.
