  We address the question of whether the quantum scale-invariant theories
introduced in [1] are renormalizable or play the role of effective field
theories that are valid below the Planck scale $M_P$. We show that starting
from two-loop level the renormalization procedure requires introduction of
counter-terms with structures different from those in the initial Lagrangian,
making these theories non-renormalizable and therefore non-predictive above
$M_P$. Despite non-renormalizability, the attractive features of these
theories, associated with the stability of the Higgs mass agains radiative
corrections and the smallness of the cosmological constant, remain intact.
