  We compute explicitly the adjoint cohomology of two N-graded Lie algebras of
maximal class (infinite dimensional filiform Lie algebras) m_0 and m_2. It is
known that up to an isomorphism there are only three N-graded Lie algebras of
the maximal class. The third algebra from this list is the "positive" part L_1
of the Witt (or Virasoro) algebra and its adjoint cohomology was computed
earlier by Feigin and Fukhs. We show that the total space H*(m_j,m_j) is
"almost" isomorphic to the completed tensor product of the algebra m_j by
scalar cohomology space H^*(m_j), j=0,2.
