A quasi-endowed fund is typically a pass-through (flow-through or expendable) fund that, for administrative purposes, is going to be considered an endowed fund.   Frequently the board will decide that, although the terms of the fund agreement clearly indicate that there is no endowed portion, they would like to grow the fund and thus will treat it like an endowed fund.   In this instance, it is typically given the same GL account structure as an endowed fund, but is given a different class code so that it can continue to be reported separately from the endowed funds.