High-order Absorbing Boundary Conditions (ABCs), applied on a rectangular artificial computational boundary that truncates an unbounded domain, are constructed for a general two-dimensional linear scalar time-dependent wave equation which represents acoustic wave propagation in anisotropic and subsonically convective media. They are extensions of the construction of Hagstrom, Givoli and Warburton for the isotropic stationary case. These ABCs are local, and involve only low-order derivatives owing to the use of auxiliary variables on the artificial boundary. The accuracy and well-posedness of these ABCs is analyzed. Special attention is given to the issue of mismatch between the directions of phase and group velocities, which is a potential source of concern. Numerical examples for the anisotropic case are presented, using a finite element scheme. © 2009 Elsevier Inc. All rights reserved.