The sigma-convergence and sigma-core of a real bounded sequence were introduced in [R. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30 (1963) 81-94] and [S.L. Mishra, B. Satapathy, N. Rath, Invariant means and a-core, J. Indian Math. Soc. 60 (1984) 151-158], respectively. In this work, we extend these ideas to double sequences. (C) 2006 Elsevier Ltd. All rights reserved.