A set of drift-reduced field-aligned magnetohydrodynamic equations is obtained for modeling the turbulent dynamics of multicomponent edge plasmas in tokamaks. A set of initial equations and approximations governing the plasma motion is given. The analysis is performed by employing the 21-moment approximation of Grad’s method (the Zhdanov closure). Mass conservation, momentum and energy balance equations for electrons and ions, as well as the plasma vorticity equation, are derived, both in conservative and non-conservative forms.