  An irreducible character $\chi$ of an association scheme is called nonlinear
if the multiplicity of $\chi$ is greater than $1$. The main result of this
paper gives a characterization of commutative association schemes with at most
two nonlinear irreducible characters. This yields a characterization of finite
groups with at most two nonlinear irreducible characters. A class of
noncommutative association schemes with at most two nonlinear irreducible
character is also given.
