The paper treats the problem of obtaining moments of the inverted Wishart distribution. The theory presented is essentially an extension of the author’s [Research Rep. No.141, Inst. Actuar. Math. and Math. Statist., Univ. Stockholm/Sweden (1985)] results and amounts to bringing forward two new approaches, one for moments of order up to three and the other for moments of arbitrary order. In the latter case recursive as well as non-recursive formulas are provided and some problems associated with these moments are discussed. The results are illustrated by an example using the growth curve model.