Various hydrodynamic approaches are used in this paper to illustrate hot-electron, non-equilibrium, and intervalley transfer effects in a two-valley semiconductor. These approaches include the single-valley, two-valley displaced Maxwellian, and the two-valley macro-kinetic hydrodynamic transport models. Results obtained from these transport models are compared with those from Monte Carlo simulations. It is found that the transport parameters and rate coefficients obtained from the displaced Maxwellian approach, in the case of no electron-electron scattering, significantly deviate from Monte Carlo results in hot-electron situations. In addition, the displaced Maxwellian distribution results in less pronounced velocity overshoot behaviour. Insufficient information on intervalley transfer in extreme non-equilibrium cases provided by the single-valley hydrodynamic model is also illustrated. Results clearly show that in non-equilibrium and hot-electron situations the single-valley approach actually provides a much better transport description for electrons in the two-valley semiconductor than the two-valley displaced Maxwellian hydrodynamic approach. Moreover, the previously developed macro-kinetic approach is shown to be in excellent agreement with the Monte Carlo method in extreme non-equilibrium and hot-electron situations.