We analyze the behavior of group and phase velocities in optical waveguides supporting strongly confined propagating modes. We discuss the implications of material absorption for electromagnetic properties of nanoguides and develop an analytical description of the interplay between geometry-induced and materials-induced dispersions. In the limit of strong confinement, the phase velocity of waveguide modes becomes vanishingly small, while group velocity can be modulated from negative to positive values. The modulation of group velocity is enhanced by the factor of λ2/R2 with respect to macroscopic systems. Both slow- and fast-light regimes can be achieved in the same nanoguiding structure, and dynamical switching between the two regimes is possible. Applications of the developed formalism lie in the field of ultrafast active nanophotonics.