Pipeline transport has been one of the progressive technologies for conveying a large quantity of bulk materials. The modern way of pipelining prefers the dense slurries, which can be in some cases directly processed without dewatering. The hydraulic transport of dense hydromixtures can bring several advantages. Compared to a mechanical transport, it is dust free, it demands substantially less space, makes possible full automatization and needs a minimum of operating staff. On the other hand, it brings higher operational pressures and considerable demands for a high quality of pumping equipment and control system. For the proper design of economical and operate safe pipelining, a good knowledge of the flow behaviour of highly concentrated slurries is necessary. The flow behaviour of highly concentrated fine-grained hydromixtures can be approximated by rheological models for laminar flow regime. These models seem to be suitable for slurry containing clay, kaolin, coal, ash, ash-gypsum tailings, metallic ores and similar materials. The rheological parameters - yield stress tau(y), fluid consistency K and flow behaviour index n - have to be determined experimentally. The flow behaviour of dense fine-grained slurries was experimentally investigated on tube viscometer with three different pipe diameters varying from D = 10.5 to 26.8 mm, for the kaolin and ash-gypsum slurry. For the turbulent regime, two models based on above mentioned rheological parameters [P. Slatter, in: Proc. 8th Conf. Transport and Sedimentation of Solid Particles, Prague, Czech Republic, 1995, p. A3; A.D. Thomas, K.C. Wilson, Can. J. Chem. Eng. 65 (1987) 335.] were analyzed.