It is shown that the eigenfunctions of the monodromy operator of the Schrod- inger operator (with a potential periodic in time and rapidly decreasing in the space variables) decay in the space variables faster than any power. The spectrum of the monodromy operator is also investigated. It is proved that 1) the monodromy operator has no singular continuous spectrum; and 2) the total number of eigenfunctions of the monodromy operator (counting multiplicity) is finite.