To　explore　the　internal　resonance　between　different　cables　and　beam　in　the　cable-stayed　bridge,　a　double-cable-stayed　beam　model　is　established　in　this　paper.　Unlike　previous　studies,　the　two　cables　have　different　frequencies.　Therefore,　it　is　possible　to　investigate　the　in-plane　one-to-one-to-two　internal　resonance　among　the　second-order　mode　of　the　beam　(global　mode)　and　the　first-order　modes　of　two　cables　(local　modes)　when　the　beam　is　subjected　to　the　primary　resonance　excitation.　Firstly,　the　partial　differential　equations　(PDEs)　governing　the　behaviors　of　the　beam　and　cables　are　discretized　using　the　Galerkin　method,　resulting　in　ordinary　differential　equations　(ODEs).　It　is　worth　noting　that　two　various　trial　functions　of　the　cables,　namely,　the　superposition　of　dragging　function　with　sinusoidal　function　(TF1)　and　real　modal　function　(TF2),　are　adopted　to　compare　the　differences　in　nonlinear　behaviors,　which　is　also　the　motivation　of　this　study.　Then,　the　multiple　time　scale　method　is　employed　to　solve　the　ODEs,　and　in　this　way,　the　corresponding　modulation　equations　are　derived.　Based　on　the　obtained　modulation　equations,　the　steady-state　solutions　are　acquired　so　as　to　discuss　the　nonlinear　characteristics　of　the　system　using　various　trial　functions.　Meanwhile,　the　accuracy　of　the　perturbation　results　is　verified　by　solving　the　ordinary　differential　equations　directly　with　the　Runge-Kutta　method.　Finally,　several　interesting　findings　and　conclusions　are　given.