  We point out that the $\mu$-problem in theories in which supersymmetry
breaking is communicated to the observable sector by gauge interactions is more
severe than the one encountered in the conventional gravity-mediated scenarios.
The difficulty is that once $\mu$ is generated by a one-loop diagram, then
usually $\bmu$ is also generated at the same loop order. This leads to the
problematic relation $\bmu \sim \mu \Lambda$, where $\Lambda \sim$ 10--100 TeV
is the effective supersymmetry-breaking scale. We present a class of theories
for which this problem is naturally solved. Here, without any fine tuning among
parameters, $\mu$ is generated at one loop, while $\bmu$ arises only at the
two-loop level. This mechanism can naturally lead to an interpretation of the
Higgs doublets as pseudo-Goldstone bosons of an approximate global symmetry.
