  We show that the Morita Frobenius number of the blocks of the alternating
groups, the finite groups of Lie type in describing characteristic, and the Ree
and Suzuki groups is 1. We also show that the Morita Frobenius number of almost
all of the unipotent blocks of the finite groups of Lie type in non-defining
characteristic is 1, and that in the remaining cases it is at most 2.
