[en] The authors consider the Cauchy problem for the nonlinear Dirac equation in one space dimension. They show that a smooth solution of this equation satisties the classical wave equation. From this property they deduce an estimation for the Lsup(infinite) space norm of the time-dependent solution, which implies the existence of a unique global solution. Furthermore they prore that the square-integrated value of the time-dependent solution tends asymptotically to zero. From this they conclude the non-existence of bound state. (HSI)