  Multisite interaction spin-S models in an external magnetic field are studied
recursively on the Bethe-like lattices. The transfer-matrix method is extended
to calculate exactly the two-spin correlation functions. The exact expressions
for the correlation length and magnetic susceptibility are derived for spin-1/2
models. The singularity of the correlation length with critical index $\nu =1$
and the proportionality of magnetic susceptibility to correlation length in the
second order phase transition region of spin-1/2 ferromagnetic models on the
Bethe-like lattices are established analytically.
