In this paper, we study \((2-d)\)-kernels in graphs. We shall show that the problem of the existence of \((2-d)\)-kernels is \(\mathcal{N}P\)-complete for a general graph. We also give some results related to the problem of counting \((2-d)\)-kernels in graphs. For special graphs, we show that the number of \((2-d)\)-kernels is equal to the Fibonacci numbers.