  We study the continuity properties of trajectories for some random series of
functions $\sum a\_kf(\alpha X\_k(\omega))$ where $a\_k$ is a complex sequence,
$X\_k$ a sequence of real independent random variables, $f$ is a real valued
function with period one and summable Fourier coefficients. We obtain almost
sure continuity results for these periodic or almost periodic series for a
large class of functions, where the "almost sure" does not depend on the
function.
