Assuming time stationarity of the one-particle distribution function F on the scale of the bounce motion of particles in a magnetic field B, we expand the Vlasov equation through O (&egr; in the adiabatic parameter &egr;, which is the ratio of particle gyroradius to scale length of the magnetic field. Since F is directly proportional to particle flux d&PHgr;/dW d&OHgr; differential in kinetic energy W and solid angle &OHgr;, F is in principle measurable in space experiments, and our analysis is tailored to be explicitly applicable to space problems. To O (1), F is gyrotropic; its first velocity moment is (if nonvanishing) parallel to B, and hence macroscopic parallel flow is included in this term. The O (&egr;) contribution is nongyrotropic, and macroscopic flow perpendicular to B plus additional parallel flow results from these terms. The degree of nongyrotropy and hence the amount of cross-field macroscopic flow depend on the perpendicular component of the electric field E, on curvature and shear in the magnetic field, and on the spatial gradient ∇Fo pitch angle derivative ∂Fo/∂Δ, and speed derivative ∂Fo/∂&ugr; of the lowest-order distribution function Fo. We also show that the usual expression for the electric field E, which produces plasma corotation in an axisymmetric system such as a dipole, also holds for any nonaxisymmetric but rigidly rotating magnetic field pattern, provided the observed magnetic field is used in place of the dipole field.