We have calculated the interaction dipole moment, polarizability and first hyperpolarizability of the dihydrogen–helium pair using flexible basis sets of Gaussian-type functions and high-level ab initio methods. Around the equilibrium position of the linear configuration (the helium-atom at a distance of R e /a 0 =6.43 from the centre of the dihydrogen molecule) the interaction mean (α¯int) and anisotropy (Δα int ) of the dipole polarizability and the mean hyperpolarizability (β¯int) vary as [α¯int(R)-α¯int(Re)]/e2a02Eh-1=0.0069(R-Re)-0.0125(R-Re)2+0.0052(R-Re)3[Δαint(R)-Δαint(Re)]/e2a02Eh-1=-0.0601(R-Re)-0.0052(R-Re)2+0.0042(R-Re)3+0.0020(R-Re)4[β¯int(R)-β¯int(Re)]/e3a03Eh-2=-1.22(R-Re)+0.68(R-Re)2-0.15(R-Re)3+0.01(R-Re)4 at the CCSD/[6s4p3d1f/6s4p3d1f] level of theory.