Using the tight-binding method we carried out the band structure calculations of hypothetical armchair (6,6), (11,11) and zigzag (20,0)-like metal-boron nanotubes consisting of the metal-boron bilayers of hexagonal diborides MB2 (M = Mg, Al, Sc, Ti). Their electronic properties and interatomic bonds are considered as a function of the composition and atomic structure of the tubes. Composite metal-boron-carbon nanotubes based on layered LiBC are also discussed.