Electrically conducting adhesive nanocomposites are obtained dispersing multiwall carbon nanotubes (MWCNT) in a thermoplastic polyurethane (TPU) by a melt mixing method. The liaison between the viscoelastic properties of the nanocomposites and their tackiness is investigated. Probe-tack results obtained at a low strain rate obey a polymer/nanotube interaction mechanism that favours tackiness, since maximum stress, strain at failure and adhesion energy increase with MWCNT concentration. However, in experiments at a high strain rate, the polymer entanglement network plays the principal role and MWCNTs only act diminishing the deformabilty of the network and reducing strain at failure and adhesion energy.