在数学中，局部系统或称局部系数是源于代数拓扑的一种观念，它是常系数的同调或上同调理论的推广。这个观念也能应用于代数几何 。

用层论的语言来讲，局部系统是局部上同构于常数层的阿贝尔群层。若此层整体来看也同构于常数层，则就回到了传统的常系数层上同调理论。例子包括了带有平坦联系的矢量丛，基本群的线性表示则给出了局部同构于矢量空间常数层的局部系统。

In mathematics, local coefficients is an idea from algebraic topology, a kind of half-way stage between homology theory or cohomology theory with coefficients in the usual sense, in a fixed abelian group A, and general sheaf cohomology which, roughly speaking, allows coefficients to vary from point to point in a topological space X. Such a concept was introduced by Norman Steenrod.