Recently, ultrafast nonlinear optical responses of single-wall carbon nanotubes (SWCNTs) in suspensions and in films have been investigated intensively. Transient photobleaching has been observed with femtosecond laser pulses at photon energies of 0.8 ~ 1.1 eV (wavelengths = 1100 ~ 1550 nm), resonant with the lowest interband transitions of semiconducting SWCNTs. Here, we report both absorptive and refractive nonlinearities in a film of multiwalled carbon nanotubes (MWCNTs) grown mainly along the direction perpendicular to the surface of quartz substrate. Such MWCNT films are prepared by a method of plasma enhanced chemical vapor deposition. By employing Z-scans with 180-fs laser pulses at wavelengths ranging from 720 to 1550 nm, we have observed that both absorptive and refractive nonlinearities are of negative. More importantly, the degenerate pump-probe measurement reveals an ultrafast recovery time of ~ 1 ps. In addition, we also present a demonstration that the ultrafast nonlinear optical properties can be manipulated by a hybrid system in which MWCNTs are coated with ZnO nanoparticles. At wavelengths of interest, it is known that ZnO possesses three-photon (or four-photon) absorption, which is of positive sign and can be used to balance off the negative nonlinearity of MWCNTs.