It is well--known that solutions of the rational interpolation problem or Newton--Padé approximation problem can be represented with the help of continued fractions if certain normality assumptions are satisfied. By comparing two interpolating continued fractions, one obtains a recursive QD-type scheme for computing the required coefficients. In this note a uniform approach is given for two different interpolating continued fractions of ascending and descending type, generalizing ideas of Rutishauser, Gragg, Claessens, and others.

In the non--normal case some of the interpolants are equal yielding so-called singular blocks. By appropriate ``skips'' in the Newton--Padé table modified interpolating continued fractions are derived which involve polynomials known from the Kronecker algorithm and from the Werner--Gutknecht algorithm as well as from the modification of the cross--rule proposed recently by the authors. A corresponding QD--type algorithm for the non--normal Newton--Padé table is presented. Finally, the particular case of Padé approximation is discussed where --- as in Cordellier's modified cross--rule --- the given recurrence relations become simpler.