Stationary, large scale plasma flows along the field lines are analyzed using the first three moments of the collisionless Boltzmann equation. The number of integrals of motion which can be found is restricted not only by the cutoff of the hierarchy of the moment equations but also by the forms of the available first-order partial differential equations which often do not satisfy Cauchy condition of integrability. Only three integrals of motion exist for the plasma continuum described by plasma density, velocity, two components of the pressure tensor and two components of the heat flow tensor. The equation for the field-aligned current, which is algebraic in j∥, is derived. It expresses the field-aligned current as function of the perpendicular electric field and perpendicular gradients of the pressure components and of the magnetic field strength determined at the investigated point of the field line. ¿ American Geophysical Union 1993