Slow slip events and associated non-volcanic tremors are sensitive to oscillatory stress perturbations, such as those induced by tides or seismic surface waves. Slow slip events and tremors are thought to occur near the seismic-aseismic transition regions of active faults, where the difference a-b =/lnV between the sensitivity of friction to slip rate and fault state, which characterizes the stability of slip, can be arbitrarily small. We investigate the response of a velocity-strengthening fault region to oscillatory loads through analytical approximations and spring-slider simulations. We find that fault areas that are near velocity-neutral at steady-state, i.e.,/lnV 0, are highly sensitive to cyclic loads: oscillatory stress perturbations in a certain range of periods induce large transient slip velocities. These aseismic transients can in turn trigger tremor activity with enhanced oscillatory modulation. In this sensitive regime, a harmonic Coulomb stress perturbation of amplitude S causes a slip rate perturbation varying as eS/(a-b), where is the effective normal stress. This result is in agreement with observations of the relationship between tremor rate and amplitude of stress perturbations for tremors triggered by passing seismic waves. Our model of tremor modulation mediated by transient creep does not require extremely high pore fluid pressure and provides a framework to interpret the sensitivity and phase of tidally modulated tremors observed in Parkfield and Shikoku in terms of spatial variations of friction parameters and background slip rate.