We have created hybrids of functionalized single wall carbon nanotubes (fSWCNTs) and also multiwall CNTs (fMWCNTs) with PBT/PTMO, a block copolymer of semicrystalline poly(butyl terephthalate) (PBT) with amorphous oxytetramethylene (PTMO). For both single wall (SW) and multiwall (MW) carbon nanotubes (CNTs) tensile modulus and strain at break as a function of CNTs’ concentration (cCNT) show maxima. Elongation at break is enhanced by the nanotubes, a plasticizing effect—much stronger for SWCNTs because they have less contact points per unit area with the matrix and also are more flexible. Repetitive tensile tests were also performed; each loading cycle resulted in lowering the tensile modulus. Brittleness B(cCNT) diagrams show minima. New results for CNT hybrids fit an earlier general diagram for determination of viscoelastic recovery in sliding wear (f) as a function of brittleness (B); the original equation with unchanged parameters covers also these results. Volumetric wear was determined after abrasion on a pin-on-disk tribometer. Minima are seen on the volumetric wear versus cCNT diagrams, similar to those on the B(cCNT) diagrams.