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Carbon-nanotube, field-effect transistors (CNFETs) are among the candidates for emerging radio-frequency applications, and improved linearity has recently been identified as one of the performance advantages they might offer. In this paper, the potential for improved linearity has been investigated by considering an array-based device structure under the best-case scenario of ballistic transport. A nonlinear equivalent circuit for ballistic field-effect transistors is used to compare the linearity of CNFETs to conventional MOSFETs. We show that nanotube devices working at high frequencies are not inherently linear, as recently suggested in the literature, and that CNFETs exhibit overall linearity that is comparable to their MOSFET counterparts. The nonlinear quantum capacitance is identified to be a major source of high-frequency nonlinearity in CNFETs. The impacts of device parameters such as oxide capacitance, channel width, and tube pitch are also investigated.