Let S(\(\gamma)\), \(\gamma\geq 0\), denote the class of distributions F satisfying \[ (i)\quad \lim_{x\to \infty}\bar F^{2*}(x)/\bar F(x)=2\int^{\infty}_{0}e^{\gamma Y}dF(y)0\), are characterized by means of subexponential densities. As an application we derive a result on the asymptotic behaviour of densities of random sums. In particular for an M/G/1 queue, we relate the tail behaviour of the stationary waiting time density to that of the service time distribution.