Summary: Nonparametric orthogonal series regression function estimation is investigated in the case of a fixed point design where the observation points are irregularly spaced in a finite interval \([a,b]\subset {\mathbb R}\). Convergence rates for the integrated mean-square error and pointwise mean-square error are obtained in the case of estimators constructed using the Legendre polynomials and Haar functions for regression functions satisfying the Lipschitz condition.