The paper studies fuzzy differential systems under generalized metric spaces approach. Let \(E^{m}\) denote the space of \(m\)-dimensional fuzzy numbers (normal, fuzzy convex, upper-semicontinuous, compactly supported fuzzy sets \(u:\mathbb{R}^{m}\rightarrow [ 0,1]).\) Existence of a unique solution for fuzzy differential systems of the form \(Y'=F(t,Y),\) \(Y(t_{0})= \bar{b},\) with \(F:[t_{0},T]\times (E^{m})^{n}\rightarrow (E^{m})^{n},\) \( \bar{b}\in (E^{m})^{n}\) is shown under different assumptions. “Linear” fuzzy differential systems of the form \(Y^{\prime }=A(t)Y,\) \(Y(t_{0})=\bar{b },\) with \(A(t)\) a matrix with real entries, and higher order fuzzy differential systems are discussed in detail.