Abstract : The paper investigates the problem of choosing between two simple hypothesis, H sub o and H sub l, in terms of independent, identically distributed random variables, when observations can be taken in groups. At any stage in the decision procedure it must be decided whether to stop or take action now or to continue, in which case the size of the next group of observations must be decided upon. The problem is to find an optimal procedure incorporating a stopping, group size (batch) and terminal action rule. It is shown that the optimal stopping rule is of the sequential probability ratio type. The special, but important, situation where the log likelihood can assume only a finite number of integral multiples of a constant, is investigated. It is shown that optimum procedures can be obtained by proper formulation of the problem in terms of Markov sequential decision schemes and solved by linear programming. Finally, a policy improvement type of routine is presented when the stopping rule is specified.