Japanese plums are classified as climacteric; however, some economically important cultivars selected in California produce very little ethylene and require long ripening both “on” and “off” the tree to reach eating-ripe firmness. To unravel the ripening behavior of different Japanese plum cultivars, ripening was examined in the absence (air) or in the presence of ethylene or propylene (an ethylene analog) following a treatment or not with 1-methylcyclopropene (1-MCP, an ethylene action inhibitor). Detailed physiological studies revealed for the first time three distinct ripening types in plum fruit: climacteric, suppressed-climacteric, and non-climacteric. Responding to exogenous ethylene or propylene, the slow-softening supressed-climacteric cultivars produced detectable amounts of ethylene, in contrast to the novel non-climacteric cultivar that produced no ethylene and softened extremely slowly. Genetic analysis using microsatellite markers produced identical DNA profiles for the climacteric cultivars “Santa Rosa” and “July Santa Rosa,” the suppressed-climacteric cultivars “Late Santa Rosa,” “Casselman,” and “Roysum” and the novel non-climacteric “Sweet Miriam,” as expected since historic records present most of these cultivars as bud-sport mutations derived initially from “Santa Rosa.” This present study provides a novel fruit system to address the molecular basis of ripening and to develop markers that assist breeders in providing high-quality stone fruit cultivars that can remain “on-tree,” increasing fruit flavor, saving harvesting costs, and potentially reducing the need for low-temperature storage during postharvest handling.