In this study, the kernel smoothing nonparametric IRT models for polytomous response testing based on standardization-normalization scoring and correlation weighting were proposed. These models can be applied to analyze the any types of heterogeneous testing with dichotomous items or polytomous items. Furthermore, these models without the constraint of local independence can be combined with the improved ordering theory for polytomous response testing proposed by Hsiang-Chuan Liu (2006) to analyze the ordering relationships of dichotomous items or polytomous items for any individual examinee.