The structure of gyroviscous forces due to the collisionless magnetic
viscosity is considered for a plasma with finite temperature gradients
and anisotropic perturbed pressure. The standard gyroviscous cancella
tion is generalized for a plasma with del T not equal 0 by including e
ffects of the third-order moments in the Braginskii's gyroviscosity te
nser. New reduced plasma-density and parallel momentum-balance equatio
ns are derived taking into account particle and heat flows along the e
quilibrium magnetic field.