  A L\'evy process is said to creep through a curve if, at its first passage
time across this curve, the process reaches it with positive probability. We
first study this property for bivariate subordinators. Given the graph
$\{(t,f(t)):t\ge0\}$ of any continuous, non increasing function $f$ such that
$f(0)>0$, we give an expression of the probability that a bivariate
subordinator $(Y,Z)$ issued from 0 creeps through this graph in terms of its
renewal function and the drifts of the components $Y$ and $Z$. We apply this
result to the creeping probability of any real L\'evy process through the graph
of any continuous, non increasing function at a time where the process also
reaches its past supremum. This probability involves the density of the renewal
function of the bivariate upward ladder process as well as its drift
coefficients. We also investigate the case of L\'evy processes conditioned to
stay positive creeping at their last passage time below the graph of a
function. Then we provide some examples and we give an application to the
probability of creeping through fixed levels by stable Ornstein-Uhlenbeck
processes. We also raise a couple of open questions along the text.
