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A new rotational viscometer is presented which can be operated up to 2 000 bar and a maximum shear stress of 420 Pa. It allows, for the first time, to investigate the non-Newtonian flow behaviour of moderately concentrated polymer solutions. Results of measurements with two representatives of the system 2-propanol/poly(butyl methacrylate) with weight-average molecular weights Mw = 520 000 and Mw = 2 050 000, and ratios of weight- to number-average molecular weights Mw/Mn = 1,08 and Mw/Mw = 1,23, resp. in the region of moderate polymer concentrations are reported. For a ca. 7 wt.-% solution of the higher-molecular-weight polymer one obtains viscometric relaxation times τ0 varying from 1 to 100 ms in the region from 1 to 2 000 bar and from 40 to 75°C; at the lower temperature the application of p can raise τ0 by one order of magnitude. The steady-state shear compliance (proportional to τ0/η0, where η0 is the zero-shear viscosity), is independent of pressure of varies only slightly. For the present system, which gels thermoreversibly upon cooling, η0 and τ0 as a function of temperature and pressure can be well represented by the Williams-Landel-Ferry equation.