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A detailed investigation of multiband superconductivity and low-frequency Leggett's plasma resonances in Mg(1-x)Al(x)B2 (0 <= x <= 0.45) system was carried out using tunneling and Andreev spectroscopy. Temperature dependences of superconducting gaps Δ_σ and Δ_π and they variation upon the degree of disorder and the Al concentration were studied. In the current-voltage characteristics (CVCs) of Mg(1-x)Al(x)B2 break junctions (SIS- type), we have observed peculiarities related to the Leggett's mode. The structure is detectable only at temperatures T<Tc and disappears with suppression of the Josephson current by an external magnetic field (which supports the above mentioned version). We have also observed a reproducible subharmonic gap structure in the CVCs of SnS (Andreev) contacts. In this case, the traditional threshold energy 2Δ_σ should be replaced by (2Δ_σ + m E_0) due to a resonant emission of 'm' Leggett's plasmons in the process of multiple Andreev reflections (MAR). The dependence of the Leggett's collective mode energy Epsilon0 upon the values of the gaps Δ_σ and Δ_π and also upon the temperature has been derived. The energy of Leggett's mode in Mg(1-x)Al(x)B2 samples was found to decrease with a reduction of Tc.