  We present the chiral truncation of the eleven dimensional M-algebra down to
ten and six dimensions. In ten dimensions, we obtain a topological extension of
the $(1,0)$ Poincar\'e superalgebra that includes super one-form and super
five-form charges. Closed super three- and seven-forms associated with this
algebra are constructed. In six dimensions, we obtain a topological extension
of the $(2,0)$ and $(1,0)$ Poincar\'e superalgebras. The former includes a
quintet of super one-form charges, and a decuplet of super three-form charges,
while the latter includes a triplet of super three-form charges.
