The purpose of this paper is to look for bubbles in the Art Market using a structure based on steady state results for TAR models and appropriate definitions of bubbles recently put forward by Knight, Satchell and Srivastava (2011). The usual method for investigating bubbles is to measure prices as deviations from fair value. We assess whether it is meaningful to define a fair value of art and conclude that it is very challenging empirically to implement any definition. We then treat fair value as zero in one instance and unobservable in the other case and in both cases provide evidence of bubbles in the art market