  We discuss gain of analyticity phenomenon of solutions to the initial value
problem for semilinear Schroedinger equations with gauge invariant
nonlinearity. We prove that if the initial data decays exponentially, then the
solution becomes real-analytic in the space variable and a Gevrey function of
order 2 in the time variable except in the initial plane. Our proof is based on
the energy estimates developed in our previous work and on fine summation
formulae concerned with a matrix norm.
