Under study is the stability of Persidskii systems with distributed delay.We assume that the sector-type functionson the right-hand sides of the system are essentially nonlinear.Also, we propose some original construction of the Lyapunov–Krasovskii functionalof use in deriving new asymptotic stability conditions of the zero solution.The approach is applied to the stability analysis of the Lurie indirectcontrol system and a mechanical system with essentially nonlinearpositional forces.Using some development of the averagingmethod, we obtain the conditions that guarantee stability undernonstationary perturbations with zero mean values for the systems under study. © 2024 Elsevier B.V., All rights reserved.