In this paper we review existing appoaches to semantics construction in LTAG (Lexicalised Tree Adjoining Grammar) which are all based on the notion of derivation (tree)s. We argue that derivation structures in LTAG are not appropriate to guide semantic composition, due to a non-isomorphism, in LTAG, between the syntactic operation of adjunction on the one hand, and the semantic operations of complementation and modification, on the other. Linear Logic based “glue” semantics, by now the classical approach to semantics construction within the LFG framework (cf. Dalrymple (1999)) allows for flexible coupling of syntactic and semantic structure. We investigate application of “glue semantics” to LTAG syntax, using as underlying structure the derived tree, which is more appropriate for principle-based semantics construction. We show how linear logic semantics construction helps to bridge the non-isomorphism between syntactic and semantic operations in LTAG. The glue approach allows to capture non-tree local dependencies in control and modification structures, and extends to the treatment of scope ambiguity with quantified NPs and VP adverbials. Finally, glue semantics applies successfully to the adjunction-based analysis of long-distance dependencies in LTAG, which differs significantly from the f-structure based analysis in LFG.