  In this paper we study a group G which is the quotient of a free product of
groups by the normal closure of a word that is contained in a in a subgroup
which has the form of a generalised triangle group.
  We use known properties of generalised triangle groups, together with
detailed analyses of pictures and of words in free monoids, to prove a number
of results such as a Freiheitssatz and the existence of Mayer-Vietoris
sequences for such groups under suitable hypotheses. The hypotheses are weaker
than those in an earlier article of Howie and Shwartz, yielding generalisations
in two directions of the results in that article.
