We show that if a solution $y(x)$ of a sub-analytic differential equation admits an asymptotic expansion $\sum_{i=1}^{\infty} c_i x^{\mu_i}$ with $\mu_i\in\mathbb{R}_+$, then the exponents $\mu_i$ belong to a finitely generated semi-group of $\mathbb{R}_+$. We deduce a similar result for the components of non-oscillating trajectories of real analytic vector fields in dimension n.