In　this　paper,　the　instability　boundaries　of　an　axially　moving　viscoelastic　beam　due　to　parametric　resonance　are　revisited　for　the　internal　resonance　case.　The　relation　between　the　time-dependent　tension　and　the　time-dependent　axial　speed　is　constructed,　which　provides　a　new　model　in　the　study　of　axially　moving　material　with　pulsation　parameters.　The　instability　boundaries　caused　by　the　combination　of　parametric　and　internal　resonances　are　studied　using　the　method　of　multiple　time　scales.　Some　strange　instability　boundaries　are　detected　when　the　internal　resonance　is　considered.　The　phenomenon　of　local　zigzag　boundary　contour　is　explained　from　the　viewpoint　of　modal　interactions.