We theoretically study the performance limits of current-gain cutoff frequency, ƒ_T, for the HEMTs with InAs or In_0.70Ga_0.30As 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, L_{g, eff}, as the corresponding length to (x). By extrapolating L_{g, eff} to L_g = 0nm, we estimate the lower limit of L_{g, eff}, L_{g, eff}⁽⁰⁾. Then we estimate the performance limit of ƒ_T, ƒ_T⁽⁰⁾, by extrapolating ƒ_T to L_{g, eff}⁽⁰⁾. The estimated ƒ_T⁽⁰⁾ are about 3.6 and 3.7THz for the HEMTs with InAs middle layers of 5 and 8nm in thickness, and about 3.0THz for the HEMT with In_0.70Ga_0.30As middle layer of 8nm in thickness, respectively. The higher ƒ_T⁽⁰⁾ in the HEMTs with InAs middle layers are attributed to the increased average electron velocity, v_d, in the channel. These results indicate the superior potential of the HEMTs using InAs in the channels. The HEMT with InAs middle layer of 8nm in thickness shows the highest ƒ_T on condition of the same L_g because of its highest v_d. However, the increased total channel thickness results in the longer L_{g, eff}⁽⁰⁾, which leads to the restriction of ƒ_T⁽⁰⁾. Therefore, in order to increase ƒ_T⁽⁰⁾, it is essential to make L_{g, eff} short in addition to making v_d high. Our results strongly encourage in making an effort to develop the HEMTs that operate in the terahertz region.