Electronic Journal of Differential Equations, Vol. 1997(1997), No. 21, pp 1-14. Title: A spectral problem with an indefinite weight for an elliptic system Author: Mamadou Sango (Univ. of the Witwatersrand, South Africa) Abstract: We establish the completeness and the summability in the sense of Abel-Lidskij of the root vectors of a non-selfadjoint elliptic problem with an indefinite weight matrix and the angular distribution of its eigenvalues. Submitted September 18, 1997. Published November 29, 1997. Math Subject Classification: 35P99, 35J55, 58G25. Key Words: indefinite weight; completeness; summability; root vectors.