We introduce a generalized cln grammar (gclng), a generalization of a completely linearly nested context-free grammar (clncfg), of which variables are partitioned linearly and each rule satisfies similar conditions as those of clncfg related to its partition. We show that the class of languages generated by gclng's coincides with the class of quasi-rational languages, and consider the inclusion relations between languages generated by gclng's and those generated by clncfg's.