The constitutive relations between stresses and heat fluxes in Couette flow and gradients of velocity and temperature, known for Maxwell molecules, are generalized for hard sphere molecules. These relations are the generalization of Newton-Fourier (Navier-Stokes) relations for shear flow with strong nonequilibrium. Similar relations are established for strong shock wave flow and for spherical expansion into vacuum for Maxwell and hard sphere molecules. General structure of constitutive relations for macroscopic description of gas flow with strong translational nonequilibrium outside the thin Knudsen boundary layers is established. Derivation is based on the hypothesis: on the solution of Boltzmann equation the stresses and heat flux depend only on velocity gradient and temperature gradient. Hamilton theorem on square dependence of arbitrary tensor function of second rank on symmetric tensor of second rank is generalized. Generalization of transport coefficients, -transport scalar function, -depends on molecular potential and on tensor invariants of symmetric and anti-symmetric parts of velocity gradient and of temperature gradient. The part of transport functions is determined by DSMC solutions of Boltzmann equation for one-dimensional flow problem.