Resonance　and　bifurcation　are　prominent　and　significant　features　observed　in　various　nonlinear　systems,　often　leading　to　catastrophic　failure　in　practical　engineering.　This　paper　investigates,　under　an　analytical　and　numerical　perspective,　the　dynamical　characteristics　of　a　fractional　Rayleigh　oscillator　with　distributed　time　delay.　Firstly,　through　the　application　of　the　multiple　scales　method,　we　derive　approximated　analytical　solutions　and　amplitude–frequency　equations　for　the　regions　near　both　primary　and　secondary　resonances.　The　stability　conditions　of　steady-state　motions　and　the　existence　region　of　the　subharmonic　response　are　also　obtained.　Furthermore,　to　validate　the　accuracy　of　the　approximated　solutions,　the　results　are　compared　with　numerical　solutions　derived　from　the　Caputo　scheme,　revealing　a　high　concordance　between　them.　Then,　a　comprehensive　study　on　response　curves　is　conducted　for　the　system　under　different　nonlinear　damping,　fractional　parameters　and　delay　strength.　Finally,　we　identify　and　discuss　the　presence　of　the　forked　bifurcation　within　the　system.　©　2024　International　Association　for　Mathematics　and　Computers　in　Simulation　(IMACS)