  We investigate electric-field effects in dilute electrolytes with nonlinear
polarization. As a first example of such systems, we add a dipolar component
with a relatively large dipole moment $\mu_0$ to an aqueous electrolyte. As a
second example, the solvent itself exhibits nonlinear polarization near charged
objects. For such systems, we present a Ginzburg-Landau free energy and
introduce field-dependent chemical potentials, entropy density, and stress
tensor, which satisfy general thermodynamic relations. In the first example,
the dipoles accumulate in high-field regions, as predicted by Abrashikin {\it
et al}.$[$Phys.Rev.Lett. {\bf 99}, 077801 (2007)$]$. Finally, we consider the
case, where Bjerrum ion pairs form a dipolar component with nonlinear
polarization. The Bjerrum dipoles accumulate in high-field regions, while
field-induced dissociation was predicted by Onsager $[$J. Chem. Phys.{\bf 2},
599 (1934)$]$. We present an expression for the field-dependent association
constant $K(E)$, which depends on the field strength nonmonotonically.
