This dissertation presents nonlinear terahertz (THz) properties of carbon nanomaterials investigated by time-resolved high-field THz spectroscopy. In order to determine THz characteristics of nanomaterials, we performed THz power spectrum measurement, THz raster imaging, THz time-domain spectroscopy (THz-TDS) and time-resolved pump-probe experiment on two different types of single layer graphene and a free standing multi-walled carbon nanotubes (MWCNTs), utilizing strong single-cycle THz pulses (central frequency, 0.9 THz; bandwidth, 1 THz; THz field amplitude, E_THz>1 MV/cm) generated by optical rectification (a second order nonlinear optical process) of femtosecond laser pulses (pulse energy, 1 mJ; pulse duration, 100 fs; repetition rate, 1 kHz) with titled pulse front for phase matching between optical and THz pulses in LiNbO3 crystal. Strong and broadband THz pulses induce transparency in two different types of single layer graphene grown by catalytic chemical vapor deposition (CVD). A substrate-free homogeneous graphene becomes more transparent to the THz radiation than an inhomogeneous graphene on silicon as the peak strength of THz field increases over 50kV/cm considered as the threshold of the nonlinear transparency effect. The experimental results show that suspended graphene is more efficient to manipulate THz signal than one with a substrate. Free-standing MWCNTs drawn from a forest of MWCNTs synthesized by CVD exhibit highly anisotropic linear and nonlinear THz responses. There are no nonlinear effects for the polarization perpendicular to the MWCNT axis, whereas, in the parallel polarization configuration, intense THz pulses induce nonlinear absorption in the quasi-one-dimensional conducting media. That is, it is revealed via time-resolved measurements of transmitted THz pulses and a theoretical analysis of the data that strong THz fields enhance permittivity in carbon nanotubes by generating charge carriers. Optical-Pump/THz-probe (OPTP) spectroscopy shows that optical pump pulses induce interband transitions in MWCNTs: Its conductivity is increased by generating photo-excited hot-carriers as optical pump energy increase. On the other hand, Optical-Pump/Intense THz-Pump spectroscopy (OPITP) exhibits three carrier dynamic phenomena which are optical pump-induced absorption, THz field-induced absorption and transparency in MWCNTs: Intense THz and optical pump energies (E_THz<538kV/cm and I_opt=103uJ/〖cm〗^2) give rise to photo-excited hot-carriers and THz field induced-carrier density via band to band transitions, however, sub-band scattering dominant in the THz-field range between 538 to 653kV/cm leads to increased effective mass, which reduces mobility of carrier.