In group sequential sampling the experimenter is allowed at each sampling stage to choose any number of new observations up to a maximum of \(m\) (positive fixed integer). The total number of observations in the experiment may or may not be required to be bounded. In the paper under review the observations \(X_ 1,X_ 2,\dots\) are i.i.d. real valued random variables with distribution \(P_ \theta\), \(\theta\in\Theta\), dominated by a fixed sigma finite measure. The number of possible terminal actions is assumed to be finite. Under mild conditions on loss- and cost-structure, and assuming a prior on \(\Theta\), the nature of Bayes procedures is investigated. If the cost for taking observations is proportional to the number of observations, then the optimal group size is 1. For other cost functions this needs not be true; e.g., if there is an overhead: cost function = constant + linear term. Such an example is given for a test of \(\theta=1\) versus \(\theta=2\) if the \(X's\) are uniform in \((0,\theta)\). Then in the continuation region the optimal group size is 1 or 2 depending on the posterior value of \(P(\theta=1)\). The example also shows that the ``onion skins'' conjecture of \textit{N. Schmitz} [ibid., 205-213 (1991)] is not true in its present form.