  Given a general critical or sub-critical branching mechanism, we define a
pruning procedure of the associated L\'evy continuum random tree. This pruning
procedure is defined by adding some marks on the tree, using L\'evy snake
techniques. We then prove that the resulting sub-tree after pruning is still a
L\'evy continuum random tree. This last result is proved using the exploration
process that codes the CRT, a special Markov property and martingale problems
for exploration processes. We finally give the joint law under the excursion
measure of the lengths of the excursions of the initial exploration process and
the pruned one.
