In a real world scenario,several complex systems are represented by a group of interdependent network systems,and not by a single network.This paper focuses on the synchronization control of corresponding nodes in two-layer heterogeneous networks with stochastic perturbations and mixed delays.Based on the LaSalle-type invariance principle and the Lyapunov stability theory,the paper derives sufficient conditions for global asymptotic synchronization by applying the pinning control,which only controls a small fraction of the nodes.To reduce the gain of feedback control,the synchronization conditions of two-layer heterogeneous networks is further weakened by adopting the adaptive control scheme.Finally,the effectiveness of the theoretical results is verified by numerical simulations.