The transport of one-speed neutrons has been studied in a homogeneous sphere with Marshak boundary conditions. The scattering function is assumed to be a combination of linearly anisotropic and strongly forward-back ward scattering. Numerical results for the critical radius are obtained and tabulated for different scattering parameters using the spherical harmonics method. We have also obtained the numerical values of the critical radius in the range of 1/c less than or equal to alpha, beta less than or equal to 1. The results indicate that the radius varies monotonically with increasing anisotropy. The monotonic variation continues and limits to a non-zero value with an extreme forward bias and linear anisotropy. Finally, sonic results are discussed and compared with those already obtained by using various methods. It is shown that the spherical harmonics method gives generally accurate results and is easily applicable to this type of anisotropic scattering kernel. (C) 2001 Elsevier Science Ltd. All rights reserved.