The hysteresis and compensation behaviors of the spin-3/2 cylindrical Ising nanotube system are studied within the framework of the effective-field theory with correlations. The effects of the Hamiltonian parameters are investigated on the magnetic and thermodynamic quantities, such as the total magnetization, hysteresis curves, and compensation behaviors of the system. Depending on the Hamiltonian parameters, some characteristic hysteresis behaviors are found, such as the existence of double and triple hysteresis loops. According to Neel classification nomenclature, the system displays Q-, R-, P-, N-, M-, and S-types of compensation behaviors for the appropriate values of the system parameters. We also compare our results with some recently published theoretical and experimental works and find a qualitatively good agreement. (C) 2014 AIP Publishing LLC.