  This paper studies the upper bound of the lifespan of classical solutions of
the initial value problems for one dimensional wave equations with quasilinear
terms of space-, or time-derivatives of the unknown function. The results are
same as those of the semilinear case. But it is quite meaningful to consider
this kind of problems for the purpose to cover the optimality of the general
theory for nonlinear wave equations by many model equations as far as possible.
