[*below*]{} the critical coupling strength. Namely, we demonstrate that these systems exhibit [*echo*]{} phenomena: If a stimulus pulse is applied at time $t=0$, followed by a second stimulus pulse at time $t=\tau $, then pulse echo responses can appear at $t=2\tau ,3\tau
,\ldots$. This phenomenon depends on both nonlinearity and memory inherent in the oscillator system, the latter being a consequence of the continuous spectrum of the linearized system.**]{}

I. Introduction
===============

Due to their occurrence in a wide variety of circumstances, systems consisting of a large number of coupled oscillators with different natural oscillation frequencies have been the subject of much scientific interest[@pikovsky01; @strogatz04]. Examples where the study of such systems is thought to be relevant are synchronous flashing of fireflies[@buck88] and chirping of crickets[@walker69], synchronous cardiac pacemaker cells[@michaels87], brain function[@singer93], coordination of oscillatory neurons governing circadian rhythms in mammals[@yamaguchi02], entrainment of coupled oscillatory chemically reacting cells[@kiss05], Josephson junction circuit arrays[@wiesenfeld95], etc. The globally-coupled, phase-oscillator model of Kuramoto[@kuramoto84; @acebron05] exemplifies the key generic feature of large systems of coupled oscillators. In particular, Kuramoto considered the case where the distribution function of oscillator frequencies was monotonically decreasing away from its peak value, and he showed that, as the coupling strength 