Summary: Let \( X\) be a metric space and \(\mu\) a finite Borel measure on \( X\). Let \(\bar{P}^{q,t}_\mu\) and \(P^{q,t}_\mu\) be the packing premeasure and the packing measure on \( X\), respectively, defined by the gauge \((\mu B(x, r))^q(2r)^t\), where \(q, t \in R\). For any compact set \( E\) of finite packing premeasure the authors prove: (1) if \(q < 0\) then \(\tilde{P}^{q,t}_\mu (E)=P^{q,t}_\mu (E)\); (2) if \(q>0\) and \(\mu\) is doubling on \( E\) then \(\tilde{P}^{q,t}_\mu (E)\) and \(P^{q,t}_\mu (E)\) are both zero or neither.