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This paper presents qualitative and bifurcation analysis near the degenerate equilibrium in a two-stage cancer model of interactions between lymphocyte cells and solid tumor and contributes to a better understanding of the dynamics of tumor and immune system interactions. We first establish the existence of Hopf bifurcation in the 3-dimensional cancer model and rule out the occurrence of the degenerate Hopf bifurcation. Then a general Hopf bifurcation formula is applied to determine thedoi:10.3934/mbe.2012.9.347 pmid:22901068 fatcat:nl3et42v5bbijk3m6plvrlxi3u