  We report the observation of an intriguing behaviour in the transport
properties of nanodevices operating in a regime between the Fabry-P\'erot and
the Kondo limits. Using ultra-high quality nanotube devices, we study how the
conductance oscillates when sweeping the gate voltage. Surprisingly, we observe
a four-fold enhancement of the oscillation period upon decreasing temperature,
signaling a crossover from single-electron tunneling to Fabry-P\'erot
interference. These results suggest that the Fabry-P\'erot interference occurs
in a regime where electrons are correlated. The link between the measured
correlated Fabry-P\'erot oscillations and the SU(4) Kondo effect is discussed.
