  This paper studies a class of nonlinear Dirac equations with cubic terms in
$R^{1+1}$, which include the equations for the massive Thirring model and the
massive Gross-Neveu model. Under the assumption that the initial data has
bounded $L^2$ norm, the global existence and the uniqueness of the strong
solution in $C([0,\infty),L^2(R^1))$ are proved.
