Exceptional points (EPs) are singularities in the spectrum of non-hermitian operators. They occur in a wide range of systems and lead to many often counterintuitive effects. One such effect is the chiral state conversion upon adiabatic, circular variation of external parameters around an EP. For one encircling direction the adiabatic theorem holds, whereas for the other direction it breaks down, resulting in a different outcome depending on the encircling direction. In this thesis we identify exceptional points in armchair and zigzag graphene nanoribbons and, subsequently, simulate dynamically encircling them. We find EPs occurring generically at the edges of a bandgap and an EP emerging non-generically at real crossings in the bandstructure of armchair ribbons. We can show that dynamical parameter variations around and in the vicinity of generic EPs yield non-hermitian effects, but no chiral state conversion. We find, however, chiral state conversion when encircling non-generic EPs for a broad spectrum of parameter paths and ribbon lengths. In the end, we conclude with comments on potential realizations in experiment.