We find a new class of cosmic string solutions with non-vanishing magnetic
flux of N = 1, D = 4 supergravity with a cosmological constant and coupled
to any number of Maxwell and scalar multiplets. We show that these magnetic
cosmic string solutions preserve 1/2 of supersymmetry. We give an explicit
example of such a solution for which the complex scalars are constant and
the spacetime is smooth with topology R-1,R-1 x S-2. Two more examples are
explored for which a complex scalar field takes values in CP1 and in SL(2,
R)/U(1). (C) 2001 Published by Elsevier Science B.V.