Characteristic properties of one-dimensionalmodels of transient gas-liquid two-phase flows in long pipelines are investigated. The methods for studying the hyperbolicity of the systems of equations of multi-fluid and drift-fluxmodels are developed. On the basis of analytical and numerical studies, the limits of the hyperbolicity domains in the space of governing dimensionless parameters are found, and the impact of the closure relations on the characteristic properties of the models is analyzed. The methods of ensuring the global unconditional hyperbolicity are proposed. Explicit formulas for the eigenvelocities of the system of the drift-flux model equations are obtained and the conclusions about their sign-definiteness are drawn.