  An equivalence between generalised restricted solid-on-solid (RSOS) models,
associated with sets of graphs, and multi-colour loop models is established. As
an application we consider solvable loop models and in this way obtain new
solvable families of critical RSOS models. These families can all be classified
by the Dynkin diagrams of the simply-laced Lie algebras. For one of the RSOS
models, labelled by the Lie algebra pair (A$_L$,A$_L$) and related to the
C$_2^{(1)}$ vertex model, we give an off-critical extension, which breaks the
Z$_2$ symmetry of the Dynkin diagrams.
