Several years ago, we found a new chemical condition for the spontaneous oscillatory contraction of glycerinated skeletal muscle and named it "SPOC". The condition was such that MgATP coexists with its hydrolytic products, MgADP and inorganic phosphate (Pi). Micromolar concentrations of free Ca2+ were not necessarily required for this oscillation. Here, we summarize our recent work on the mechano-chemical properties of SPOC not only in glycerinated single fibers and myofibrils of skeletal muscle (fast type) but also in glycerinated small bundles of cardiac muscle; the isometric tension and its oscillation were examined at various concentrations of MgATP, MgADP and Pi while controlling the concentration of free Ca2+; we constructed a three-dimensional "state diagram" taken against the concentrations of MgADP, Pi and free Ca2+. The 3-D state diagram clearly showed the existence of three regions corresponding to three muscular states; the SPOC region was located in between the regions for contraction (without oscillation) and relaxation. Based on these results, we discuss the mechanism of SPOC, especially the minimum requirements for its occurrence. Finally, we suggest that slow shortening and quick lengthening repeatedly occur every half-sarcomere through the transition between the two states, where weak-force-generating complexes or strong-force-generating complexes are dominant; the transition may be induced by a coupling with the mechanical states of cross-bridges and/or thin filaments.