We continue studying the existence of uniform L ∞ a priori bounds for positive solutions of subcritical elliptic equationsWe provide sufficient conditions for having a-priori L ∞ bounds forC 1,µ (Ω) positive solutions to a class of subcritical elliptic problems in bounded, convex, C 2 domains.In this part II, we extend our results to Hamiltonian elliptic systemsand p, q are lying in the critical Sobolev hyperbolae 1 p+1 + 1 q+1 = N -2 N .For quasilinear elliptic equations involving the p-Laplacian, there exists a-priori bounds for positive solutions of (P) p when f (u) = u p ⋆ -1 /[ln(e + u)] α , with p * = N p/(Np), and α > p/(Np).We also study the asymptotic behavior of radially symmetric solutions u α = u α (r) of (P) 2 as α → 0.