Flat Expansions of Solutions to ODEs at Singularities

We consider plane polynomial systems of ODEs at degenerate nonmonodromial singularities. We investigate the solutions passing through the singularity which in the first approximation are given by power series with an exponential addition. These solutions are uniquely determined as truncated series of arbitrary length in flat functions, which generalizes the notion of exponential addition. These series can converge or diverge. However even in the case of divergence they possess good approximative properties.