This work deals with the study of effect of multiwalled carbon nanotubes (MWNT) on the tensile hysteresis behavior of carboxylated nitrile rubber composites under various cyclic strain levels (5, 25, and 300%). The presence of thermo‐labile ionic crosslinks as well as interfacial stick‐slip motion of filler in the matrix was found to enhance both Mullins effect and hysteretic damping. Hysteretic damping reached a maximum of 37% for 0.050 volume fraction of MWNT at medium strain (25%). The crosslink density measured through equilibrium swelling method revealed that the degree of ionic crosslinking decreased with increase in MWNT content, which was confirmed by infrared spectroscopy. Transmission electron microscopic images showed that agglomeration of nanotubes was prominent at higher volume fractions of MWNT. Acoustic absorption capability, as measured by the impulse method, decreased with increase in MWNT concentration. The high hysteretic damping and low acoustic absorption make the nanocomposites a superior choice for structural vibration damping in underwater acoustic sensor systems. POLYM. COMPOS., 39:E1269–E1279, 2018. © 2018 Society of Plastics Engineers