The radiation environment in space is complex in terms of both the variety of charged particles and their dose rates. Simulation of such an environment for experimental studies is technically very difficult. However, with the variety of beams available at the National Space Research Laboratory (NSRL) at Brookhaven National Laboratory (BNL) it is possible to ask questions about potential interactions of these radiations. In this study, the end point examined was transformation in vitro from a preneoplastic to a neoplastic phenotype. The effects of 1 GeV/n iron ions and 1 GeV/n protons alone provided strong evidence for suppression of transformation at doses ≤5 cGy. These ions were also studied in combination in so-called mixed-beam experiments. The specific protocols were a low dose (10 cGy) of protons followed after either 5–15 min (immediate) or 16–24 h (delayed) by 1 Gy of iron ions and a low dose (10 cGy) of iron ions followed after either 5–15 min or 16–24 h by 1 Gy of protons. Within experimental error the results indicated an additive interaction under all conditions with no evidence of an adaptive response, with the one possible exception of 10 cGy iron ions followed immediately by 1 Gy protons. A similar challenge dose protocol was also used in single-beam studies to test for adaptive responses induced by 232 MeV/n protons and ¹³⁷Cs γ radiation and, contrary to expectations, none were observed. However, subsequent tests of 10 cGy of ¹³⁷Cs γ radiation followed after either 5–15 min or 8 h by 1 Gy of ¹³⁷Cs γ radiation did demonstrate an adaptive response at 8 h, pointing out the importance of the interval between adapting and challenge dose. Furthermore, the dose–response data for each ion alone indicate that the initial adapting dose of 10 cGy used in the mixed-beam setting may have been too high to see any potential adaptive response.