We discuss the bicriterion stochastic knapsack problem. It is described as follows. We have a known capacity of some resource, and a finite set of projects. Each project requires some units of the resource which is not known in advance, but given by a discrete probability distribution with a finite number of outcomes. The resource requirements become known when a project has been selected. Given, that a project has been selected two rewards are received (corresponding to two objective functions), which only depend on the project chosen (the rewards are independent of the resource required). The goal is to design a set of resource adaptive strategies for sequentially choosing the projects such that the total expected value of the two objective functions is maximized, i.e. the complete set of nondominated solutions are found. We also present preliminary experimental results.