A nonrigid rotor model is developed from the two-parameter quantum algebra $U_{qp}({\rm u}_2)$. [This model presents the $U_{qp}({\rm u}_2)$ symmetry and shall be referred to as the qp-rotor model.] A rotational energy formula as well as a qp-deformation of E2 reduced transition probabilities are derived. The qp-rotor model is applied (through fitting procedures) to twenty rotational bands of superdeformed nuclei in the $A \sim 130$, 150 and 190 mass regions. Systematic comparisons between the qp-rotor model and the q-rotor model of Raychev, Roussev and Smirnov, on one hand, and a basic three-parameter model, on the other hand, are performed on energy spectra, on dynamical moments of inertia and on B(E2) values. The physical signification of the deformation parameters q and p is discussed.