In this paper, we give an algorithm which finds, for an integer base $$b\ge 2$$ , all squarefree integers $$d\ge 2$$ such that sequence of X-components $$\{X_n\}_{n\ge 1}$$ of the Pell equation $$X^2-dY^2=\pm 1$$ has two members which are base b-repdigits. We implement this algorithm and find all the solutions to this problem for all bases $$b\in [2,100]$$ .