  The Grishchuk--Zel'dovich effect is the contribution to the microwave
background anisotropy from an extremely large scale adiabatic density
perturbation, on the standard hypothesis that this perturbation is a typical
realization of a homogeneous Gaussian random field. We analyze this effect in
open universes, corresponding to density parameter $\Omega_0<1$ with no
cosmological constant, and concentrate on the recently discussed
super-curvature modes. The effect is present in all of the low multipoles of
the anisotropy, in contrast with the $\Omega_0=1$ case where only the
quadrupole receives a contribution. However, for no value of $\Omega_0$ can a
very large scale perturbation generate a spectrum capable of matching
observations across a wide range of multipoles. We evaluate the magnitude of
the effect coming from a given wavenumber as a function of the magnitude of the
density perturbation, conveniently specified by the mean-square curvature
perturbation. From the absence of the effect at the observed level, we find
that for $0.25\leq\Omega_0\leq 0.8$, a curvature perturbation of order unity is
permitted only for inverse wavenumbers more than one thousand times the size of
the observable universe. As $\Omega_0$ tends to one, the constraint weakens to
the flat space result that the inverse wavenumber be more than a hundred times
the size of the observable universe, whereas for $\Omega_0 < 0.25$ it becomes
stronger. We explain the physical meaning of these results, by relating them to
the correlation length of the perturbation. Finally, in an Appendix we consider
the dipole anisotropy and show that it always leads to weaker constraints.
