  We develop the technique of Thermodynamic Bethe Ansatz to investigate the
ground state and the spectrum in the thermodynamic limit of the staggered $XXZ$
models proposed recently as an example of integrable ladder model. This model
appeared due to staggered inhomogeneity of the anisotropy parameter $\Delta$
and the staggered shift of the spectral parameter. We give the structure of
ground states and lowest lying excitations in two different phases which occur
at zero temperature.
