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We prove that Kergin interpolation polynomials and Hakopian interpolationpolynomials at the points of a Leja sequence for the unit disk $D$ of asufficiently smooth function $f$ in a neighbourhood of $D$ converge uniformlyto $f$ on $D$. Moreover, when $f$ is $C^\infty$ on $D$, all the derivatives ofthe interpolation polynomials converge uniformly to the correspondingderivatives of $f$.

On the Convergence of Kergin and Hakopian Interpolants at Leja Sequences for the Disk