We investigate -cohomology of some commutative cooperation algebras associated with certain periodic cohomology theories. For KU and , the Adams summand at a prime , and for KO we show that -cohomology vanishes above degree 1. As these cohomology groups are the obstruction groups in the obstruction theory developed by Alan Robinson we deduce that these spectra admit unique structures. As a consequence we obtain an structure for the connective Adams summand. For the Johnson--Wilson spectrum with we establish the existence of a unique structure for its -adic completion.