  We propose a coupled system of fast and slow phase oscillators. We observe
two-step transitions to quasi-periodic motions by direct numerical simulations
of this coupled oscillator system. A low-dimensional equation for order
parameters is derived using the Ott-Antonsen ansatz. The applicability of the
ansatz is checked by the comparison of numerical results of the coupled
oscillator system and the reduced low-dimensional equation. We investigate
further several interesting phenomena in which mutual interactions between the
fast and slow oscillators play an essential role. Fast oscillations appear
intermittently as a result of excitatory interactions with slow oscillators in
a certain parameter range. Slow oscillators experience an oscillator-death
phenomenon owing to their interaction with fast oscillators. This oscillator
death is explained as a result of saddle-node bifurcation in a simple phase
equation obtained using the temporal average of the fast oscillations. Finally
we show macroscopic synchronization of the order 1:m between the slow and fast
oscillators.
