Abstract: Let $\Lambda$ be a finite-dimensional $k$-algebra over a field $k$. The low dimensional Hochschild cohomological groups $H^i(\Lambda)~(i \leq 2)$ have a classical interpretation and play an important role in representation theory
of finite-dimensional algebras. In this note the formulae on the dimensions of the first and the second Hochschild cohomology groups of $l$-hereditary algebras are obtained explicitly.

Key words: l-hereditary algebra, Hochschild cohomology, Marked couple