This　work　investigates　the　synchronization　problems　of　a　two-layered　network,　where　the　involved　nodes　are　of　delay　nonlinearity.　By　using　a　generalized　delay　differential　inequality,　some　sufficient　conditions　are　established　for　reaching　synchronization　between　the　two　layers.　It　is　revealed　that　when　the　inter-layer　coupling　strength　is　time-varying,　the　time　average　of　the　smallest　eigenvalue　of　an　induced　matrix　plays　a　key　role　in　reaching　synchronization.　Meanwhile,　the　largest　admissible　delay　is　also　estimated.　Numerical　examples　are　also　given　to　demonstrate　the　validity　of　the　theoretical　results.　©　2019　IEEE.