  We study the neutral minima of two-Higgs doublet models, showing that these
potentials can have at least two such minima with different depths. We analyse
the phenomenology of these minima for the several types of two-Higgs doublet
potentials, where CP is explicitly broken, spontaneously broken or preserved.
We discover that it is possible to have a neutral minimum in these potentials
where the masses of the known particles have their standard values, with
another deeper minimum where those same particles acquire different masses.
