  We determine the position and the type of spontaneous singularities of
solutions of generic analytic nonlinear differential systems in the complex
plane, arising along antistokes directions towards irregular singular points of
the system. Placing the singularity of the system at infinity we look at
equations of the form $\mathbf{y}'=\mathbf{f}(x^{-1},\mathbf{y})$ with
$\mathbf{f}$ analytic in a neighborhood of $(0,\mathbf{0})$, with genericity
assumptions; $x=\infty$ is then a rank one singular point. We analyze the
singularities of those solutions $\mathbf{y}(x)$ which tend to zero for $x\to
\infty$ in some sectorial region, on the edges of the maximal region (also
described) with this property. After standard normalization of the differential
system, it is shown that singularities occuring in antistokes directions are
grouped in nearly periodical arrays of similar singularities as $x\to\infty$,
the location of the array depending on the solution while the (near-) period
and type of singularity are determined by the form of the differential system.
