  In this paper we address the problem of consistently construct Langevin
equations to describe fluctuations in non-linear systems. Detailed balance
severely restricts the choice of the random force, but we prove that this
property together with the macroscopic knowledge of the system is not enough to
determine all the properties of the random force. If the cause of the
fluctuations is weakly coupled to the fluctuating variable, then the
statistical properties of the random force can be completely specified. For
variables odd under time-reversal, microscopic reversibility and weak coupling
impose symmetry relations on the variable-dependent Onsager coefficients. We
then analyze the fluctuations in two cases: Brownian motion in position space
and an asymmetric diode, for which the analysis based in the master equation
approach is known. We find that, to the order of validity of the Langevin
equation proposed here, the phenomenological theory is in agreement with the
results predicted by more microscopic models.
