A graph is called signed if there is a designation of its edges as either positive or negative. The signed degree of a vertex \(v\) is the number of positive edges through \(v\) less the number of negative edges through \(v\). The degree sequence consists of signed degrees of all vertices in nonincreasing order. Using ``derived'' sequences the authors find a convenient necessary and sufficient condition for a given nonincreasing finite sequence of nonzero integers to be the degree sequence of some signed graph. Derived sequences arise by substracting one from some initial members and adding one to some last members of the given sequence. There is a lot of nice concrete examples in the paper: signed paths, stars, double stars, complete signed graphs. Very interesting is also the so-called \(H\)-procedure, yielding many further results.