A statistical theory was proposed for the degradation (random scission of chains) of a network having f-functional nodes in the case where all chains contain equireactive groups and a chain scission event does not create new groups or suppress more than one group. Closedform relations were established between the conversion ratio of the degradation process and the crosslink density. Emphasis was put on the value of the conversion ratio for which the gel disappears. Some limited cases already considered in the literature were recovered, but a general solution was proposed for networks having any number of reactive groups per chain, be it uniform or not, and for conversion ratios up to the degelation point. The results were applied successfully to recent experiments regarding the hydrolysis of a polyester.