The rising need for hybrid physical platforms has triggered a renewed interest in the development of agile radio-frequency phononic circuits with complex functionalities. The combination of traveling waves with resonant mechanical elements appears as an appealing means of harnessing elastic vibration. In this work, we demonstrate that this combination can be further enriched by the occurrence of traveling surface acoustic waves (SAWs), induced by elastic nonlinearities, interacting with a pair of otherwise linear micron-scale mechanical resonators. Reduction of the resonator-gap distance and an increase in the SAW amplitude results in a frequency softening of the resonator-pair response that lies outside the usual picture of geometrical Duffing nonlinearities. The dynamics of the SAW excitation scheme allows further control of the resonator motion, notably leading to circular-polarization states. These results may pave the way toward versatile high-frequency phononic microelectromechanical-systems–nanoelectromechanical-systems circuits fitting both classical and quantum technologies.