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SUMMARYIn order to reveal the mechanism behind the ion channel diseases of muscles, we numerically analyzed bifurcations in the space-clamped HodgkinHuxley equations for muscles of frogs (HHM). The leakage conductance g l and the sodium channel effective bias voltage V m BB B were selected as bifurcation parameters. We continued codimension-one bifurcation branches of saddle node, homoclinic, Hopf, double cycle on the V m BB B u g l plane. We showed the existence of codimension-two bifurcation points: a twisted resonant, a BogdanovTakens, an inclination-flip (if), a degenerate Hopf, and a cusp. The first three were found for HHM with parameters within a realistic range. The if point is found to be a key point in the behavior of HHM, around which the parameter plane is separated into three regions: normal action potential, repetitive firing (myotonia), and depolarized resting potential (periodic paralysis). The characteristics of if are not as yet completely revealed theoretically, so our results are also of mathematical interest.