[en] Fluid models for toroidal plasma are considered paying particular attention to the effects of particle motion along the equilibrium magnetic field. It is shown that the basic fluid equations can be obtained either as moments of the drift-kinetic equation, or from the standard fluid equations by expanding them in 1/B small parameter. It is shown that the collisionless gyroviscosity accounts for the effects of the particle magnetic drift in the parallel component of the momentum balance equation. Simple truncated model of the plasma response for arbitrary ω_D (magnetic drift frequency) and k_parallelV_t (parallel transit frequency) is proposed. In the absence of resonances, which can be inhibited by the particle magnetic drift, this model recovers the exact kinetic results with satisfactory accuracy. In general case, the kinetic closure for the effects of the particle motion along the magnetic field is suggested in terms of the parallel viscosity and the heat flux. They are directly calculated from the linear drift-kinetic equation. Simplified expressions in the different asymptotic limits are derived