The possibility of reduction of wrongly triggered relay protection in earthed middlevoltage power networks is analized. In addition, middle-voltage power networks earthed by means of common lowresistence resistor are treated. By switching the transformer in parallel operation transition takes place in the connection between the neutral points of transformers which causes unnecessary operation of the earthing resistor relay protection. An detailed analization of mentioned problem is given in chapter one. The solution of earthing via a lowresistence resistor by using common scheme of earthing and protection of the resistor is treated in the next chapter. Theoretical grounds of the switching current of the transformer is given in the third section. In the next chapter are shown the results of the research of the current values on the connections between the neutral points of the transformers for cases of switching on the transformer, short-term lack of primary voltage and earth faults. The action of the relay protection is analized. The possibility of resistor protection by using the appropriate inverse I-t characteristics is analized in the last ninth section. It's been proposed protection of the resistor by using digital relays which involve more protectional functions by which is brought the complete resistor protection considering its thermical characteristics. By using digital relays with correct configuration and parameters is achieved a minimum of wrongly triggered relay protection in the circuit of resistor protection is achieved.