In this perper. ci non-linear control scheme fiw tile TCSC (thyristor-c~ontrollecl series compensator) to deimpen power oscillations and to improve the trcinsient stability of power systems is presentecl. Based on an one-mcichirze-irifnite-btis system, CI non-linear mrithematiccil model is estciblished which is proven as an ciflnr nonlinenr system. With the help of the feeclbtick 1ineriri:ation technique, the ctffine non-linear model is e.ractly tninsferred to a linecir moclel, and then the control scheme is designeclfor the TCSC based on the global linearizcition, where the input signeil uses local meeisrirements onlv. The e~j+ctivene.s.s ant1 roblrstness of the proposed non-linecir control scheme nre detnmn.strcitetl with cin one-mtdiine test svstem, where the TCSC modell i t i s cind power system simtilations Lire perfr,rmecl by itsing the progrcitn system NETOMAC. I n compeiriwn with ( I conventioncrl control scheme. significtint improvements of clwomiccil performnnce in the test power ' sv.stem (ire cichieved bv the proposeel non-lineor control strcitegy fiw the TCSC.