InAlAs/InGaAs high electron mobility transistors (HEMTs) lattice-mismatched on GaAs substrates have been fabricated with a 0.6-mu m-thick step-graded InyAl1-yAs buffer layer and a low-source-resistance triple cap layer. A peak extrinsic transconductance of 1060 mS/mm was obtained for a device with a 0.16-mu m-long gate due to both the low source resistance of 0.35 Omega mm brought by the triple cap layer and the high quality In0.5Ga0.5As channel brought by the step-graded InyAl1-yAs buffer layer. This transconductance is comparable to or higher than that of HEMTs lattice-matched on InP substrates. A maximum oscillation frequency, f(max), of 127 GHz and a cutoff frequency, f(t), of 47 GHz were obtained for a fully-passivated device with a 0.66-mu m-long gate, giving a high f(max)/f(t) ratio of 2.7. This f(max) is comparable to those of HEMTs lattice-matched on InP with the same gate length.