We have considered theoretically the waveguide properties of a plane two-layered waveguide, whose one layer is a usual magnetodielectric (forward-wave medium), but another one is a slab of so-called backward-wave material (BW-material), whose both permittivity and permeability are negative. We have analyzed the properties of eigenwaves in this waveguide. In particular, it was found that there exist waves of both TE and TM polarizations, whose fields decay exponentially from the interface of the two slabs inside both layers, and their slow-wave factor tends to infinity at small frequencies. Thus, this waveguiding system supports superslow waves with extremely short wavelengthes, as compared to the free-space wavelength and the cross section size. Other peculiarities of the spectrum are also discussed.