  We theoretically consider coherence times for spins in two quantum computer
architectures, where the qubit is the spin of an electron bound to a P donor
impurity in Si or within a GaAs quantum dot. We show that low temperature
decoherence is dominated by spin-spin interactions, through spectral diffusion
and dipolar flip-flop mechanisms. These contributions lead to 1-100 $\mu$s
calculated spin coherence times for a wide range of parameters, much higher
than former estimates based on $T_{2}^{*}$ measurements.
