This paper addresses the delayed (or anechoic) source separation problem in the case of parameterized deterministic sources. An alternating least square scheme is proposed to estimate the source parameters, the mixing coefficients and the delays. For the challenging delay parameter we adapt a sparse approximation strategy. A first algorithm considers discrete delays; then an extension, inspired by the recent sparse deconvolution literature, allows for continuous delay estimation. Numerical simulations demonstrate the effectiveness of the proposed algorithms compared to state-of-the-art methods for highly correlated Gaussian sources.