We study the almost sure asymptotic properties of the local time of the uni
form empirical process. In particular, we obtain two versions of the law of
the iterated logarithm for the integral of the square of the local time. I
t is interesting to note that the corresponding problems for the Wiener pro
cess remain open. Properties of L-P-norms of the local time are studied. We
also characterize the joint asymptotics of the local time at a fixed level
and the maximum local time.