  We prove the persistence of analyticity for classical solution of the Cauchy
problem for quasilinear wave equations with analytic data. Our results show
that the analyticity of solutions, stated by the Cauchy-Kowalewski and
Ovsiannikov-Nirenberg theorems, lasts till a classical solution exists.
Moreover, they show that if the equation and the Cauchy data are analytic only
in a part of space-variables, then a classical solution also is analytic in
these variables. The approach applies to other quasilinear equations and
implies the persistence of the space-analyticity (and the partial
space-analyticity) of their classical solutions.
