  We develop polarization observables for the processes $\gamma N\to\pi\pi N$
and $\pi N\to\pi\pi N$, using both a helicity and hybrid helicity-transversity
basis. Such observables are crucial if processes that produce final states
consisting of a spin-1/2 baryon and two pseudoscalar mesons are to be fully
exploited for baryon spectroscopy. We derive relationships among the
observables, as well as inequalities that they must satisfy. We also discuss
the observables that must be measured in `complete' experiments, and briefly
examine the prospects for measurement of some of these observables in the near
future.
