Terahertz heterodyne spectrometer using a quantum cascade laser Appl. Phys. Lett. 97, 161105 (2010) We present the design and capabilities of a high-resolution, decade-spanning ASynchronous OPtical Sampling (ASOPS)-based TeraHertz Time-Domain Spectroscopy (THz-TDS) instrument. Our system employs dual mode-locked femtosecond Ti:Sapphire oscillators with repetition rates offset locked at 100 Hz via a Phase-Locked Loop (PLL) operating at the 60th harmonic of the ∼80 MHz oscillator repetition rates. The respective time delays of the individual laser pulses are scanned across a 12.5 ns window in a laboratory scan time of 10 ms, supporting a time delay resolution as fine as 15.6 fs. The repetition rate of the pump oscillator is synchronized to a Rb frequency standard via a PLL operating at the 12th harmonic of the oscillator repetition rate, achieving milliHertz (mHz) stability. We characterize the timing jitter of the system using an air-spaced etalon, an optical cross correlator, and the phase noise spectrum of the PLL. Spectroscopic applications of ASOPS-THz-TDS are demonstrated by measuring water vapor absorption lines from 0.55 to 3.35 THz and acetonitrile absorption lines from 0.13 to 1.39 THz in a short pathlength gas cell. With 70 min of data acquisition, a 50 dB signal-to-noise ratio is achieved. The achieved root-mean-square deviation is 14.6 MHz, with a mean deviation of 11.6 MHz, for the measured water line center frequencies as compared to the JPL molecular spectroscopy database. Further, with the same instrument and data acquisition hardware, we use the ability to control the repetition rate of the pump oscillator to enable THz frequency comb spectroscopy (THz-FCS). Here, a frequency comb with a tooth width of 5 MHz is generated and used to fully resolve the pure rotational spectrum of acetonitrile with Doppler-limited precision. The oscillator repetition rate stability achieved by our PLL lock circuits enables sub-MHz tooth width generation, if desired. This instrument provides unprecedented decade-spanning, tunable resolution, from 80 MHz down to sub-MHz, and heralds a new generation of gas-phase spectroscopic tools in the THz region. C 2015 AIP Publishing LLC. [http://dx