  We present analytical and numerical results on the joint dynamics of two
coupled Duffing oscillators with nonlinearity of opposite signs (hardening and
softening). In particular, we focus on the existence and stability of
synchronized oscillations where the frequency is independent of the amplitude.
In this regime, the amplitude--frequency interdependence (a--f effect) ---a
noxious consequence of nonlinearity, which jeopardizes the use of
micromechanical oscillators in the design of time--keeping devices--- is
suppressed. By means of a multiple time scale formulation, we find approximate
conditions under which frequency stabilization is achieved, characterize the
stability of the resulting oscillations, and compare with numerical solutions
to the equations of motion.
