Studied in this paper is the exponential stability of the following nonautonomous delayed linear equation
with , . Applying the comparison method based on a Bohl-Perron-type theorem, the authors obtain some new stability conditions on exponential stability of (). These conditions are in “iterative” and “limit” forms. The results are compared with some existing ones by several examples. The study is a continuation of the paper of the authors [J. Math. Anal. Appl. 314, No. 2, 391–411 (2006; Zbl 1101.34057)], where ordinary differential equations are applied as comparison equations, while in this paper under review delay differential equations with positive coefficients and a positive fundamental function are used for comparison.