It is shown that existing neoclassical theories in the high collisionality regime are inadequate to describe the edge plasma, where the gradient length scales are of the order of (only) a few centimeters (the ''edge'' is defined here in relation to the neutrals ionization depth). Gyrostresses indeed modify considerably the continuity, energy, and parallel momentum equations if, as is usually the case, LAMBDA1 = nu(i) (qR)2/OMEGA(i)L(psi)r is not negligible compared to unity (L(psi)=L(N), L(T), L(V), where, e.g., L(N) is the density length scale). Particle transport, moreover, is no longer automatically ambipolar: the radial electric field -delV is actually determined by the ambipolarity constraint. Another parameter also usually erroneously considered to be smaller than unity is LAMBDA2 = (m(e)/m(i))1/2 (qRnu(i)/c(i))2. The theory presented here encompasses the more general conditions, where LAMBDA1 approximately 1, LAMBDA2 approximately 1.