The authors report the experimental results of ferromagnetic resonance (FMR) of the two-dimensional randomly mixed systems K2Cu1-xCoxF4 and K2Cu1-xMnxF4 with very low concentration of CO2+ and Mn2+, respectively. Both the resonance field and the linewidth show strong angular variation in the c plane having fourfold symmetries; the easy axes are parallel to the (110) directions in the unit cell of K2NiF4-type structure and the linewidth is greatest along the hard axes, i.e the (100) directions. These anisotropic behaviours are enhanced when the concentration of Co2+ (Mn2+) is increased. It is worth noting an early report by Yamazaki et al. that the FMR line of K2CuF4 has a very small fourfold anisotropic behaviour in the c plane; the easy axes are parallel to the (100) directions and the linewidth is greatest along the easy axes, contrary to the present results of the mixed systems. The angular behaviour of the FMR line observed in the diluted system K2Cu1-xZnxF4 are substantially similar to that of K2CuF4.