Although the matrix element of the gluon spin operator in nucleon helicity
states is known to be independent of some special choices of gauge, we show
that it is not invariant under a general gauge transformation. We find tha
t there exists a simple means of obtaining the matrix element in a differen
t choice of gauge from a calculation made in one specific gauge. Similar co
nclusions hold for other manifestly gauge-dependent operators present in th
e QCD angular momentum operator. [S0556-2821(99)05123-1].