The evolution of spherically symmetric unstable scalar field configurations (``bubbles'') is examined for both symmetric (SDWP) and asymmetric (ADWP) double-well potentials. Bubbles with initial static energies $E_0\la E_{\rm crit}$, where $E_{\rm crit}$ is some critical value, shrink in a time scale determined by their linear dimension, or ``radius''. Bubbles with $E_0\ga E_{\rm crit}$ evolve into time-dependent, localized configurations which are {\it very} long-lived compared to characteristic time-scales in the models examined. The stability of these configurations is investigated and possible applications are briefly discussed.tic time-scales in the models examined. The stability of these configurations is investigated and possible applications are briefly discussed.

10 pages, LaTeX (uses revtex 3.0), 4 figures (postscript files of figs.1 and 2 appended starting on line 497), report DART-HEP-93/05