Kzero--Anti-Kzero and Bzero--Anti-Bzero Constraints On Technicolor

I propose a resolution of the strong CP problem of quarks based on vacuum alignment in theories of dynamically broken electroweak and flavor symmetries. Mixing in the neutral B and K--meson systems is used to restrict the form of quark mass and mixing matrices and to constrain the masses of the topcolor gauge bosons V_8 and Z' to be greater than 5 TeV. The K^0 mixing parameter epsilon is calculated for models whose quark mass matrix leads to weak, but not strong, CP violation. It is easy to accomodate its value in some models while, in others, no reasonable combination of extended technicolor and topcolor masses can account for epsilon.