Abstarct: Let G = ( V , E ) be a graph. Assume that l and k are two non-negative integer numbers. An l-sum flow on a graph G is an assigment of non-zero real numbers to the edges of G such that for every vertex v of G the sum of values of all edges incident with v equals l. An l-sum k-flow is an l-sum flow with values from the set { ±1,…, ±(k – 1) }. In this thesis, we first study zero-sum flow in regular graphs. Next, we show that a graph of order n with a zero-sum flow has a zero-sum (n + 3)2-flow. Finally, we prove that every r-regular graph of even order admits a one-sum 5-flow.