Wind forces on structures that can be considered stiff are usually cal
culated by using the so-called gust factor G that magnifies the effect
s of the statical part of the wind speed U. In the expression of G a p
eak factor g is introduced to account for the maxima of the response d
ynamical displacement X-d(t), which is a zero mean stationary Gaussian
process. The peak factor is derived by assuming that the upcrossings
of a given level are a Poisson process, which is deemed very conservat
ive by several authors. Thus, other ways for computing g are proposed
herein, preserving its classical definition. They are: (1) the use of
the envelope of the response process; (2) the solution of the backward
Kolmogorov equation; (3) the use of some approximate formulae such as
those by Preumont, Lutes et at, and Vanmarcke. The theoretical models
are applied to the response of a linear SDOF oscillator for two value
s of the ratio of critical damping. Tn the last part of the paper a no
nlinear response, that of a Duffing oscillator, is considered and the
problem of the peak factor for this nonlinear case is attacked by usin
g the stochastic averaging of energy envelope. The results of the vari
ous approaches are compared with those obtained by numerical simulatio
n.