From the summary: We discuss the identification of material parameters occurring in isotropic incompressible hyperelasticity relations of generalized polynomial-type. The underlying strain-energy function depends on the first and second invariant of left Cauchy-Green tensor in the form of a polynomial. The material parameters are polynomial coefficients. This leads in several identification processes to linear least-square problems. However, in most applications the parameters are not restricted to a range of validity. This article points out that the assumption of merely positive material parameters leads to a non-negative strain-energy function in any process which is underpinned by requirements with respect to gradient and convexity behaviour in certain deformations. Furthermore, it is shown that for positive material parameters no non-monotonic behaviour occurs in simple deformation processes under consideration outside the identification region. The second topic of the article deals with some identification applications of tension-torsion tests.