We theoretically study the performance limits of current-gain cutoff frequency, fT, for the HEMTs with InAs or In0.70Ga0.30As middle layers in the multi-quantum-well (MQW) channels by means of the quantum-corrected Monte Carlo (MC) method. We calculate the distribution of the delay time along the channel, τ(x), and define the effective gate length, Lg,eff, as the corresponding length to τ(x). By extrapolating Lg,eff to Lg = 0 nm, we estimate the lower limit of Lg,eff, Lg(0),eff. Then we estimate the performance limit of fT, fT(0), by extrapolating fT to Lg,eff(0). The estimated fT(0) are about 3.6 and 3.7 THz for the HEMTs with InAs middle layers of 5 and 8 nm in thickness, and about 3.0 THz for the HEMT with In0.70Ga0.30As middle layer of 8 nm in thickness, respectively. The higher fT(0) in the HEMTs with InAs middle layers are attributed to the increased average electron velocity, υd, in the channel. These results indicate the superior potential of the HEMTs using InAs in the channels. The HEMT with InAs middle layer of 8 nm in thickness shows the highest fT on condition of the same Lg because of its highest υd. However, the increased total channel thickness results in the longer Lg,eff(0), which leads to the restriction of fT(0). Therefore, in order to increase fT(0), it is essential to make Lg,eff short in addition to making υd high. Our results strongly encourage in making an effort to develop the HEMTs that operate in the terahertz region.