Experimental melt data are compared with differential constitutive equations that contain only a single adjustable parameter, besides the parameters describing the linear relaxation spectrum. These include the equations of Giesekus, Phan‐Thien and Tanner, Johnson and Segalman, White and Metzner, Larson, and Aciernoet al.The deformations are step shear, step biaxial extension, and start up of steady uniaxial extension of HDPE without long side branches and LDPE with long side branches. The Johnson‐Segalman and White‐Metzner models fail to predict the experimental data accurately. The equation of Aciernoet al.shows strong oscillations in elongation and shear. The Giesekus equation fits the uniaxial extension and shear data but fails to do so for biaxial extension regardless of the choice of the adjustable parameter. The models of Phan‐Thien and Tanner and of Larson seem to fit the data best. These two equations give a reasonably good fit to the data in all three deformations for the HDPE for a single value of the adjustable parameter. For the branched LDPE, a fit is only obtained if the parameter is separately adjusted for each of the three types of deformation.