In industry, the use of large centrifugal compressors is widespread inmany vital applications such as petrochemical, natural gas distribution,and fertilizers. The increasing rate for using suc_h machines implies toconsider them as the backbone of the production process. In theseprocesses, profitability can rest directly upon the efficiency and operabilityof the plant’s compressor. The continuous monitoring and control of thesemachines are important factors influencing the efficiency and reliability of them. In the present work, the performance of a centrifugal compressor isanalyzed in order to identify the operation instability during surge androtating stall. A mathematical model is proposed in order to predict surgeas a transient phenomenon. This model requires the identification of thecompressor performance during steady state and reverse flow. So, anothermathematical model is also proposed to predict the performance duringsteady state operation and reversed flow. The proposed model is a modifiedversion of the model presented by Galvas [NASA TN D-7487, 1973]. Themodified model has a higher coefficient of correlation than Galvas’ model.Moreover, this model predicts the performance of multi-stage centrifugalcompressors, multi-compressors arranged in series and the reverse flow.This model was highly recommended to be proposed because themeasurements of the reverse flow performance is very difficult specially inindustrial compressors. Consequently, the integration between theproposed models results in an essential tool for studying the dynamic andsteady state performance of industrial multi-stage centrifugalcompressors.In order to validate the proposed models, the results are comparedwith multiple published experimental data of different compressors.Moreover, the results are also compared with multiple theoretical modelsproposed by other authors. The models are used to simulate theperformance of multi-stage centrifugal compressors. In real operatingconditions, the fertilizer sector was selected where multi-stage centrifugalcompressors are used.o.11