  In this paper, we study a class of strongly degenerate ultraparabolic
equations with analytic coefficients. We demonstrate that the Cauchy problem
exhibits an analytic smoothing effect. This means that, with an initial datum
belonging to the Sobolev space $H^s$ (of real index s), the associated Cauchy
problem admits a unique solution that is analytic in all spatial variables for
any strictly positive time. This smoothing effect property is similar to that
of the Cauchy problem for uniformly parabolic equations with analytic
coefficients.
