  We establish integral tests and laws of the iterated logarithm at 0 and at
$+\infty$, for the upper envelope of positive self-similar Markov processes.
Our arguments are based on the Lamperti representation, time reversal arguments
and on the study of the upper envelope of their future infimum due to Pardo
\cite{Pa}. These results extend integral test and laws of the iterated
logarithm for Bessel processes due to Dvoretsky and Erd\"os \cite{de} and
stable L\'evy processes conditioned to stay positive with no positive jumps due
to Bertoin \cite{be1}.
