Nest Representations of TAF Algebras A nest representation of a strongly maximal TAF algebra $A$ with diagonal $D$ is a representation $\pi$ for which $\lat \pi(A)$ is totally ordered. We prove that $\ker \pi$ is a meet irreducible ideal if the spectrum of $A$ is totally ordered or if (after an appropriate similarity) the von Neumann algebra $\pi(D)''$ contains an atom. Keywords:nest representation, meet irreducible ideal, strongly maximal TAF algebraCategories:47L40, 47L35