By choosing appropriate microemulsion systems, hexagonal cobalt (Co) and cobalt-nickel (1:1) alloy nanoparticles have been obtained with cetyltrimethylammonium bromide as a cationic surfactant at 500 degrees C. This method thus stabilizes the hcp cobalt even at sizes (<10 nm) at which normally fcc cobalt is predicted to be stable. On annealing the hcp cobalt nanoparticles in H(2) at 700 degrees C we could transform them to fcc cobalt nanoparticles. Microscopy studies show the formation of spherical nanoparticles of hexagonal and cubic forms of cobalt and Co-Ni (1:1) alloy nanoparticles with the average size of 4, 8 and 20 nm, respectively. Electrochemical studies show that the catalytic property towards oxygen evolution is dependent on the applied voltage. At low voltage (less than 0.65 V) the Co (hexagonal) nanoparticles are superior to the alloy (Co-Ni) nanoparticles while above this voltage the alloy nanoparticles are more efficient catalysts. The nanoparticles of cobalt (hcp and fcc) and alloy (Co-Ni) nanoparticles show ferromagnetism. The saturation magnetization of Co-Ni nanoparticles is reduced compared to the bulk possibly due to surface oxidation.