The XY-model (S = 1/2) on the one-dimensional superlattice (closed cha
in) is considered. The exact solution of the model is obtained by usin
g a generalized Jordan-Wigner transformation and the Green function te
chnique. Special attention is given to the study of the excitation spe
ctrum and the results are compared with those obtained by using the tr
ansfer matrix technique for the ferromagnetic case only. The thermodyn
amic properties are also studied and an explicit solution for the inte
rnal energy is presented.