This presentation focused on the grammatical property of adverbial clefts on the basis of Mizuguchi's (1999) work for clefted adverbs. We discussed the possibility of extending his proposal of VP-internal nature of clefted adverbs. Noting that there is a parallelism in cleftability between adverbs and adverbial clauses, we hypothesized that such clauses also conform to the proposal, and as a result of syntax-based considerations, we concluded that they indeed resped the hypothesis. Furthermore, based on the observation that other adverbials like adverbial NPs respect VP-internality, we advanced a more comprehensive hierarchical generalization for the cleftability of adverbials in general, incorporating Mizuguchi's proposal. Considering that adverbials are syntactic adjuncts in tree structures, which are realized as various syntactic categories, this revised generalization can be rephrased as the one for adjunct clefts. Moreover, in the sense that this generalization constrains ill-formed adjunct clefts freely generated by phrase structure rules proposed in Emonds (1970; 1976), it can be conduded that it is also a syntactic condition on the adjunct cleft formation.