The rheological properties of polypropylene melts were investigated in oscillatory shear flow, capillary rheometry, and uniaxial elongation at constant tensile stress as well as constant strain rate. At small stresses the steady-state elongational viscosity of linear conventional polypropylene has the threefold value of the shear viscosity. With increasing stress both the shear and elongational viscosity decrease. The transient elongational viscosity at constant strain rate is equal to the threefold value of the linear viscoelastic stressing viscosity as calculated from the relaxation time spectrum. In contrast, long chain branched polypropylene shows a maximum in the steady-state elongational viscosity and pronounced strain hardening in experiments at constant strain rate above an elongation of epsilon = 1. These phenomena are obtained by less than three branches per molecule. The description of the strain hardening by means of the Lodge model underestimates the measured data at deformation rates less than epsilon = 0.2 s-1. An improvement is obtained by adding a rubber-like stress component to the tensile stress.