We present results concerning the synthesis of FexCo1-x (0 < x < 1) alloy nanoparticles (NPs) with different compositions by the chemical reduction technique and subsequent structural (XRD patterns), morphological (TEM images) and magnetic (VSM magnetometry) characterization. We have got excellent quality NPs in the cubic bcc structure showing a room temperature magnetization as high as 235 emu/g for the Fe66Co34 composition alloy. Powder of composition Fe47Co53 was used to fabricate a magnetorheological fluid (MRF) by using mineral oil as carrier liquid and Aerosil 300 as additive to control the viscosity of the fluid. This MRF showed a strong magnetorheological response with a superior performance under applied magnetic field up to 616.7 kA/m and good reversibility after demagnetization process. At that highest applied magnetic field, we determined a yield stress value of 2729 Pa, that competes well with the best ones reported in the most recent literature.