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The aim of this paper is to generalize the $m-$Segre invariant for vectorbundles to coherent systems. Let $X$ be a non-singular irreducible complexprojective curve of genus $g$ over $\mathbb{C}$ and $(E,V)$ be a coherentsystem on $X$ of type $(n,d,k)$. For any pair of integers $m, t$, $0 < m < n$,$0 \leq t \leq k$ we define the $(m,t)-$Segre invariant, denoted by$S^\alpha_{m,t}$ and show that $S^\alpha_{m,t}$ induces a semicontinuousfunction on the families of coherent systems. Thus, $S^\alpha_{m,t}$ gives astratification of the moduli space $G(\alpha;n,d,k)$ of $\alpha-$stablecoherent systems of type $(n,d,k)$ on $X$ into locally closed subvarieties$G(\alpha;n,d,k;m,t;s)$ according to the value $s$ of $S^\alpha_{m,t}$. Westudy the stratification, determine conditions under which the different strataare non-empty and compute their dimension.

Segre invariant and a stratification of the moduli space of coherent systems