The term complex here refers to the intermediate area between homogeneously and heterogeneously flowing slurries. Typical examples are residual products ("tailings") from the mining industry with average particle sizes of 20 to 100 microns. The performance derating are of special interest when centrifugal slurry pumps are applied to these slurries at high solids concentrations. The Hydraulic Institute's slurry (ANSI/HI 2005) and viscous Newtonian liquid (ANSI/HI 2004) standards are briefly covered with focus on applicable viscosities for non-Newtonian slurry behaviour. Various experimental results are discussed and found to give maximum deratings in head and efficiency of about 10 and 15 %, respectively, provided stable head curves can be maintained. Magnified shock losses, circulatory flows and blockage of slurry and possibly vapour tendencies in the pump entrance region may be considered as  mechanisms behind unstable head curves together with the flow behaviour of the slurry.