OUTLINE: Randomized study. Patients are initially stratified as STANDARD RISK (tumor volume at diagnosis < 100 ml) and HIGH RISK (tumor volume at diagnosis at least 100 ml or, if < 100 ml, metastasis present). All patients receive 14 courses of chemotherapy, administered q 3 weeks throughout protocol treatment. Standard-risk patients receive 4 courses of NEOADJUVANT CHEMOTHERAPY on Regimen A, while high-risk patients are randomized on Arms I and II for 4 courses of neoadjuvant chemotherapy. LOCAL THERAPY is usually initiated on week 12, after 4 courses of neoadjuvant chemotherapy, and consists of either total removal of the tumor-bearing compartment, intracompartmental surgery (with or without adjuvant radiotherapy), or definitive radiotherapy alone; the choice is dictated by the site, tumor size, and patient age, among other variables. Postoperatively, all patients receive 10 courses of ADJUVANT CHEMOTHERAPY (plus adjuvant radiotherapy when given); standard-risk patients are randomized on Arms III and IV, while high-risk patients receive the same regimen to which they were assigned at initial randomization. When given, adjuvant radiotherapy begins on week 19 and is administered concurrently with chemotherapy. As a variant of this general plan, patients with < 50% regression of the soft tissue component of their tumors at restaging after 2 courses of neoadjuvant chemotherapy (slow response) may receive preoperative irradiation, beginning on week 7, concomitantly with the third and fourth courses of chemotherapy. The following acronyms are used: CTX Cyclophosphamide, NSC-26271 DACT Dactinomycin, NSC-3053 DOX Doxorubicin, NSC-123127 IFF Ifosfamide, NSC-109724 Mesna Mercaptoethane sulfonate, NSC-113891 VCR Vincristine, NSC-67574 VP-16 Etoposide, NSC-141540 NEOADJUVANT CHEMOTHERAPY. Regimen A (Standard risk): Alternating 3-Drug Combination Chemotherapy Regimens. VAIA: VCR/DOX/IFF alternating with VCR/DACT/IFF. Arm I (High risk): Alternating 3-Drug Combination Chemotherapy Regimens. VAIA: VCR/DOX/IFF alternating with VCR/DACT/IFF. Arm II (High-risk): Alternating 4-Drug Combination Chemotherapy Regimens. EVAIA: VP-16/VCR/DOX/IFF alternating with VP-16/VCR/DACT/IFF. LOCAL THERAPY. Surgery: Resection of entire tumor-bearing compartment, including bone and soft tissue, when possible, is the treatment of choice. The range of possible surgical procedures includes: radical resection (e.g., amputation), wide resection (en bloc removal of the entire tumor-bearing compartment), marginal surgery (en bloc removal, but resection line runs through pseudocapsule and microscopic residual disease is likely), intralesional resection (tumor incised with contamination of surgical field), and no resection. Radiotherapy: There are 3 settings in which radiotherapy is delivered in these patients: as definitive treatment when definitive surgery is not feasible, as postoperative adjuvant treatment, and preoperatively in patients with a slow response to neoadjuvant chemotherapy. Patients who are to receive definitive and postoperative adjuvant treatment are randomized between conventional fractionation and hyperfractionated accelerated split-course delivery; individuals receiving preoperative irradiation are not randomized for radiotherapy schedule but are assigned nonrandomly to receive the hyperfractionated accelerated split-course scheme (conventional fractionation requires that DOX and DACT be eliminated from concomitant chemotherapy, whereas these agents can be continued during the hyperfractionated schedule). Individual institutions may elect not to randomize for the radiotherapy fractionation scheme, i.e., to treat all patients on one schedule or the other; in such institutions, all patients must follow the same scheme, decided upon prior to treatment of the first patient. Use of photons with energies of 4-6 MV (including Co60) is recommended for extremity lesions, and 6-15 MV energies are recommended for trunk lesions; electrons may be considered for small superficial boosts, but are not adequate as a sole modality. ADJUVANT THERAPY. Arm III (Standard risk): Alternating 3-Drug Combination Chemotherapy Regimens. VACA: VCR/DOX/CTX alternating with VCR/DACT/CTX. Arm IV (Standard risk): Alternating 3-Drug Combination Chemotherapy Regimens. VAIA: VCR/DOX/IFF alternating with VCR/DACT/IFF. High-risk patients continue with 10 additional courses of VAIA or EVAIA according to original randomization. Adjuvant Radiotherapy, when administered, begins on week 19, and is given concomitantly with chemotherapy.