Many cytotoxic drugs may harm the fertility of young women treated for cancer. The aim of the study is to investigate if the Gonadotropin-Releasing Hormone agonist (GnRHa) during cancer treatment can preserve the fertility of young female cancer subjects. Approximately 300 women with newly diagnosed breast cancer and up to 200 women with newly diagnosed lymphoma, acute leukemias or sarcomas will be recruited before start of cancer treatment. The patients will be randomised in between treatment with triptorelin (experimental) or placebo (control) intramuscularly a 1:1 ratio during chemotherapy. The injections may be given once monthly or once three months depending on type of chemotherapy given. Randomisation and study drug is blinded, neither investigator, research nurse nor patient will know if it is active drug or placebo. The only person who knows is the nurse preparing the injection. Patients will be followed up to 5 years after end of treatment with physical examinations, vital signs, biochemical markers, bone mineral density exams, ultrasound for antral follicle counts and ovarian doppler flow, concomitant medications, adverse events and quality of life questionnaires.