  The XY model (s=1/2) on the one-dimensional alternating superlattice (closed
chain) is solved exactly by using a generalized Jordan-Wigner transformation
and the Green function method. Closed expressions are obtained for the
excitation spectrum, the internal energy, the specific heat, the average
magnetization per site, the static transverse susceptibility and the two-spin
correlation function in the field direction at arbitrary temperature. At T=0 it
is shown that the system presents multiple second order phase transitions
induced by the transverse field, which are associated to the zero energy mode
with wave number equal to 0 or $\pi$. It is also shown that the average
magnetization as a function of the field presents, alternately, regions of
plateaux (disordered phases) and regions of variable magnetization (ordered
phases). The static correlation function presents an oscillating behaviour in
the ordered phase and its period goes to infinity at the critical point.
