  We present a microscopic model for alpha'-NaV2O5. Using an extended Hubbard
model for the vanadium layers we derive an effective low-energy model
consisting of pseudospin Ising chains and Heisenberg chains coupled to each
other. We find a ``spin-Peierls-Ising'' phase transition which causes charge
ordering on every second ladder and superexchange alternation on the other
ladders. This transition can be identified with the first transition of the two
closeby transitions observed in experiment. Due to charge ordering the
effective coupling between the lattice and the superexchange is enhanced. This
is demonstrated within a Slater-Koster approximation. It leads to a second
instability with superexchange alternation on the charge-ordered ladders due to
an alternating shift of the O sites on the rungs of that ladder. We can explain
within our model the observed spin gap, the anomalous BCS ratio, and the
anomalous shift of the critical temperature of the first transition in a
magnetic field. To test the calculated superstructure we determine the
low-energy magnon dispersion and find agreement with experiment.
