A novel solvent extraction process, the Universal Extraction (UNEX) process, has been developed for the simultaneous separation of cesium, strontium, and the actinides from acidic waste solutions. The UNEX process solvent consists of chlorinated cobalt dicarbollide for the extraction of ¹³⁷Cs, polyethylene glycol for the extraction of ⁹⁰Sr, and diphenyl-N,N-dibutylcarbamoyl phosphine oxide for the extraction of the actinides and lanthanides. A nonnitroaromatic polar diluent consisting of phenyltrifluoromethyl sulfone has been developed for this process. A UNEX flowsheet consisting of a single solvent extraction cycle has been developed as a part of a collaborative effort between the Khlopin Radium Institute (KRI) and the Idaho National Engineering and Environmental Laboratory (INEEL). This flowsheet has been demonstrated with actual acidic radioactive tank waste at the INEEL using 24 stages of 2-cm diameter centrifugal contactors installed in a shielded cell facility. The activities of ¹³⁷Cs, ⁹⁰Sr, and the actinides were reduced to levels at which a grout waste form would meet NRC Class A LLW requirements. The extraction of ⁹⁹Tc and several nonradioactive metals by the UNEX solvent has also been evaluated.