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I was wondering, how to solve such a system with mathematica? I found the NDsolve function, but in the reference is not mentioned if it is possible to solve a system of equations.

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sol = NDSolve[{
    x'[t] == -x[t - Pi] + y'[t - 1],
    y'[t] == -y[t - Pi] - x'[t - 1],
    x[t /; t <= 0] == Cos[t],
    y[t /; t <= 0] == Sin[t]}, {x, y}, {t, 0, 18}];

Plot[Evaluate[{x'[t], y'[t]} /. First[sol]], {t, 0, 18}, PlotRange -> All]

enter image description here

ParametricPlot[Evaluate[{y'[t], x'[t]} /. First[sol]], {t, 0, 18}]

enter image description here

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