AbstractMuch theoretical work has been done in the past to represent the angular dependence in the scattering source term of the Boltzmann equation by means of Legendre or other series expansions. However, relatively little work has been done to feed this information into our present-daySNcodes. TheSNtransport codes at LASL allow a representation of anisotropy in the scattering source term by means of multi-table cross-section sets and two formalisms are given here to generate these sets. Both involve the expansion of scattering cross sections in a series of Legendre polynomials, and incorporation of the expansion coefficients in the tables of transfer cross sections. One, called a consistentPapproximation, involves a simple truncation of the series; while the other, called an extended transport approximation, includes an attempt to approximate the next higher term in the series. A general expression is derived for the error in the neutron flux due to either approximation. The numerical evaluation ofSNcross-section entries for these formalisms has been computerized.Convergence with respect to Number of Tables is numerically investigated for several different neutron-transport problems: a) deep penetration of high-energy neutrons in air; b) critical size of an enriched-uranium bare sphere; c) reflector savings for an enriched-uranium sphere immersed in H2O; and d) fast-reactor core mockup on ANL's ZPR-III.It is concluded from these problems that both approximations converge rapidly with increasing number of tables and that the simple transport approximation gives quite accurate results for a wide range of problems.