The data of tensile creep and recovery tests for a complex polyester yarn under two-step and four-step loading programs obtained by the authors are presented. Their analysis was carried out in order to study viscoelastic and viscoplastic properties of polyester yarns. The applicability of the physically nonlinear Maxwell type viscoelastoplastic constitutive equation governed by two material functions (which have been studied in detail in a series of articles) to the description of the polyester yarn behavior was examined. It was found that the basic applicability indicators of the constitutive equation found earlier are fulfilled with sufficiently small errors. It has been established that the measured values of the steady-state creep rates and plastic strain magnitudes in creep and recovery tests under different prescribed stress levels (tensile load levels) depended on stress as power functions, i.e. their dependences on stress are well approximated by linear functions in log-scale. Thus, the performance of specific applicability indicators for the model with power-law material functions was verified. The material functions for polyester yarn were determined in the class of power functions, i.e. four parameters specifying a pair of power-law material functions were found, using the family of five creep and recovery curves under different load levels. Two identification techniques were developed for the constitutive equation under consideration, realized and compared. The second technique improves the first one by the preliminary reduction (via approximation) of test creep and recovery curves to the qualitative form of theoretical creep and recovery curves generated by the constitutive relation. Verification of the calibrated model with the found power-law material functions was implemented based on the data of tensile tests of polyester yarn under four different four-steps loading test programs lasting for eight hours. It was shown that the calibrated model fits the test data for polyester yarn under rather complex loading programs sufficiently well.