A set of near-isogenic lines (NILs) of melon ( Cucumis melo L.) was used to test the relationship between the climacteric pattern and postharvest disorders at harvest and after 30 days at 8 °C. The NILs contained different chromosome introgressions in the linkage group III from the non-climacteric exotic Korean accession PI 161375 transferred into the genetic background of the non-climacteric Spanish cultivar ‘Piel de Sapo’ (PS). A quantitative trait locus (QTL) in this linkage group induced climacteric behavior in eight NILs accompanied by a peak of ethylene production and fruit dehiscence to different degrees. The cultivar ‘Nicolás’ and one NIL showed a non-climacteric pattern of respiration rate and ethylene production. The climacteric NILs were used to test the relationship between this pattern and postharvest disorders. The reference climacteric lines ‘Fado’ and ‘Védrantais’ were more sensitive to CI and associated Cladosporium rot than the NILs or PS. In general, a more intense climacteric behavior was accompanied by fruit dehiscence, and higher total losses and greater skin scald after storage, than in PS. A higher incidence of chilling injury (CI) in the climacteric NILs was found compared with the non-climacteric ones, although with exceptions (one NIL for CI in the form of scald; the same NIL and one more for pitting). The climacteric onset and netting scald were not related, and CI in the form of skin spots was only found in climacteric NILs and was positively correlated with the maximum peak of ethylene production. Some climacteric NILs did not follow the rule of a higher susceptibility to other disorders and decay after storage compared with PS, such as for example in fruit over-ripening (detected externally or internally), Cladosporium rot at the peduncle and Alternaria rot. Mealiness was independent of climacteric behavior. Three climacteric NILs obtained better flavor scores after storage than PS, although the maximum peak of ethylene production was positively correlated with off-flavor. Genotypic correlation between disorder data and the physiological data of climacteric fruit revealed positive (flavor index) or negative postharvest consequences (skin injuries, rots or off-flavors). At least one QTL can be assigned to most of the quality traits analyzed.