Summary The question as to whether autologous stem cell transplantation (SCT) after consolidation chemotherapy improves the probability of survival of patients with acute myeloid leukaemia (AML) in first remission has not been settled. Here, we present the results of a phase III study conducted in newly diagnosed adult AML patients aged <60 years. Patients who had reached a complete remission (CR) after two courses of induction chemotherapy and who were not eligible for a human leucocyte antigen‐matched sibling SCT ( n = 130), were randomized after a third consolidation cycle of chemotherapy between high‐dose cytotoxic treatment and autologous bone marrow transplantation or no further treatment. No significant differences in disease‐free survival and overall survival were observed between the two treatment arms. A slightly better overall survival in the no further treatment arm was because of fewer deaths in the first CR and a significantly better overall survival after the first relapse. The results are discussed in relation to the generic problems of applying autologous transplantation and in the perspective of the limited statistical power of this and other previously published studies.