Huyi Hu, Lai-Sang Young Nonexistence of SBR Measures for some Diffeomorphisms that are ``Almost Anosov'' (31K, TeX) ABSTRACT. The purpose of the paper is to present some simple examples that are hyperbolic everywhere except at one point, but which do not admit SBR measures. Each example has a fixed point at which the larger eigenvalue is equal to one and the smaller eigenvalue is less than one.