It is known that the implicational fragment of the relevant logic E is 
complete with respect to the class of Urquhart's models, 
where a model consists of a semilattice and a set of possible worlds.
This paper shows that some implicational relevant logics, 
which are obtained from E by adding axioms, 
are complete with respect to the class of Urquhart's models
with certain conditions.
To show this, we introduce labelled sequent calculi.