  In the paper, the problem of the existence of the maximum likelihood estimate
and the REML estimate in the variance components model is considered. Errors in
the proof of Theorem 3.1 in the article of Demidenko and Massam (Sankhy\=a 61,
1999), giving a necessary and sufficient condition for the existence of the
maximum likelihood estimate in this model, are pointed out and corrected. A new
proof of Theorem 3.4 in the Demidenko and Massam's article, concerning the
existence of the REML estimate of variance components, is presented.
