ABSTRACT: In this work, we apply the spherical harmonic expansion technique to the nonclassical transport equation, deriving a system of equations for the nonclassical flux moments, which in this work are called nonclassical spherical harmonic approximations (NSHA). The nonclassical transport equation represents a recently developed mathematical model that enables the modeling of transport problems where the particle flux does not undergo exponential attenuation. Our approach to solving the resulting system involves employing a Spectral Approach (SA) technique to represent the nonclassical angular flux moments as a truncated series of Laguerre polynomials with respect to the free-path variable s. This formulation yields a structured system of equations for the nonclassical angular flux moments akin to the classical P_N equations. Notably, we demonstrate that the NSHA framework is reduced to the classical P_N equation in a special case, highlighting the versatility and applicability of the proposed approach. To validate the derivation and assess the accuracy of NSHA, numerical results for slab geometry test problems are provided. These numerical simulations serve to verify the accuracy and efficacy of the derived equations in capturing the nonclassical transport behavior and further underscore the potential applications of NSHA in practical transport problems. We also analyze the effects of different boundary conditions, including Marshak Boundary Conditions, Mark Boundary Conditions, Asymptotic/Variational (A-V) Boundary Conditions, and Federighi-Pomraning (F-P) Boundary Conditions. Through this analysis, we aim to provide an initial assessment of how these boundary conditions influence the performance and accuracy of the NSHA. By examining these different approaches, we can explore their impact on nonclassical particle transport.