The authors derive a representation of a solution of nonlinear delay differential equations using a so-called multidelayed matrix exponential, which generalizes the results of D. Y. Khusainov
and G. V. Shuklin
[Stud. Univ. Žilina, Math. Ser. 17, No. 1, 101–108 (2003; Zbl 1064.34042
)] for autonomous linear delay systems with one delay defined by permutable matrices. In addition, sufficient conditions for exponential stability of the trivial solution of nonlinear delay differential equations with several delays for different types of nonlinearities are presented. Finally, an application of one of the stability criteria to a biological model is provided.