  The caustics of Fourier integral operators are defined as caustics of the
corresponding Schwartz kernels (Lagrangian distributions on $X\times Y$). The
caustic set $\Sigma(C)$ of the canonical relation $C$ is characterized as the
set of points where the rank of the projection $\pi:C\to X\times Y$ is smaller
than its maximal value, $dim(X\times Y)-1$. We derive the $L\sp p(Y)\to L\sp
q(X)$ estimates on Fourier integral operators with caustics of corank 1 (such
as caustics of type $A\sb{m+1}$, $m\in\N$). For the values of $p$ and $q$
outside of certain neighborhood of the line of duality, $q=p'$, the $L\sp p\to
L\sp q$ estimates are proved to be caustics-insensitive.
  We apply our results to the analysis of the blow-up of the estimates on the
half-wave operator just before the geodesic flow forms caustics.
