  We consider the (real) nonlinear wave equation $$\Box u + m^2 u + \lambda u^3
= 0, \quad m > 0, \quad \lambda > 0, $$ on four-\-dimensional Minkowski space.
We introduce the complex structure and show that the (nonlinear) operator of
dynamics, the wave and scattering operators define complex analytic maps on the
space of initial Cauchy data with finite energy. In other words, let
$R(\varphi, \pi) = \varphi + i\mu^{-1}\pi$ be the map of initial data on the
positive frequency part of the solution of the free Klein-\-Gordon equation
with these initial data. The operators $RU(t)R^{-1},$ $RWR^{-1},$ and
$RSR^{-1}$ are defined correctly and are complex analytic on the complex
Hilbert space $H^1({\R}^3,\C).$
