  In this paper, we study the global existence of steady subsonic Euler flows
through infinitely long nozzles which are periodic in $x_1$ direction with the
period $L$. It is shown that when the variation of Bernoulli function at some
given section is small and mass flux is in a suitable regime, there exists a
unique global subsonic flow in the nozzle. Furthermore, the flow is also
periodic in $x_1$ direction with the period $L$. If, in particular, the
Bernoulli function is a constant, we also get the existence of subsonic-sonic
flows when the mass flux takes the critical value.
