The polyester diol obtained from the glycolysis of the recycled PET flakes was used to synthesize the polyurethanes of PU‐1, PU‐1.7, and PU‐2 that the numbers indicate the isocyanate to hydroxyl groups (NCO/OH) molar ratios. The nanocomposites of PUs with hydroxylated multiwalled carbon nanotube (MWCNT) (PUCNT‐1.7 and PUCNT‐2) were synthesized via in situ polymerization, while the PUCNT‐1 was not synthesized due to the steric hinderance effect of MWCNT. It was shown that the NCO/OH molar ratios and the added MWCNT govern the crosslink degree of the samples. Because, the good creep–recovery behavior of the under‐loaded polymers in long time applications has remarkable importance for polymer engineers, the creep–recovery behavior of PUs and their nanocomposites was studied by dynamic mechanical analysis (DMA). Nevertheless, there has been no report on the creep–recovery behavior of these PET originated polyurethanes. The well‐known models of Power law and Burgers (for fitting the creep experimental data), and Weibull model (for fitting the recovery experimental data) showed the good agreements with the empirical data. The creep strain of the samples was in the order PU‐1 > PUCNT‐1.7 > PU‐2 > PU‐1.7 > PUCNT‐2. It was found that the crosslink‐degree of the samples and also the opposing effects of MWCNT (the reinforcing and hindrance effects) are the important parameters that govern Young modulus, creep, and recovery of the samples. PU‐1.7 due to its higher crosslink‐degree showed the lower creep–recovery strain in comparison to PU‐2 and PU‐1. The lower creep–recovery strain of PUCNT‐2 as compared to other samples can be attributed to the dominant reinforcing effect of MWCNT in this sample, whereas the high creep–recovery strain of PUCNT‐1.7 was assigned to the dominant hindrance effect of MWCNT. POLYM. COMPOS., 39:E1013–E1024, 2018. © 2017 Society of Plastics Engineers