  The Barut-Girardello coherent states (BG CS) representation is extended to
the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson
realizations. The sp(N,R) BG CS take the form of multimode ordinary
Schr\"odinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n
canonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode
Hilbert space and the relation between the canonical CS and the u(p,q) BG-type
CS representations is established. The sets of u(p,q) and sp(N,R) BG CS and
their discrete superpositions contain many states studied in quantum optics
(even and odd N-mode CS, pair CS) and provide an approach to quadrature
squeezing, alternative to that of intelligent states. New subsets of weakly and
strongly nonclassical states are pointed out and their statistical properties
(first- and second-order squeezing, photon number distributions) are discussed.
For specific values of the angle parameters and small amplitude of the
canonical CS components these states approaches multimode Fock states with one,
two or three bosons/photons. It is shown that eigenstates of a squared
non-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of
the quadratures of A.
