In recent years, the islanded electric power system of Cyprus is facing significant challenges. The increased penetration of Renewable Energy Sources (RES) in combination with the reduced reliance on conventional generators and the changes in the consumption profiles, lead to a plethora of problems widely related to low-inertia grids. These challenges vary during the different seasons of the year, due to different demand and generation conditions. Several security problems related to frequency, voltage, and fault levels are already observed in the system. The scheduled future increase of RES penetration will lead to deterioration of the system security - if adequate measures are not taken. In this paper, we present the existing problems observed in the Cyprus power system along with an overview of the expected problems due to future RES levels. Finally, we briefly discuss solution mechanisms.