This paper elaborates a class of linear L-infinity approximation algorithms generated by phi-weighted partial sums of biorthogonal expansion in Laguerre and Kautz basis. This problem arises typically as the first step of the "two-step" identification under H-infinity criterion. Bounds on the the partial sum operators and on the L-infinity norm of the approximation error are derived. A frequency domain identification procedure is proposed where the model parameters are computed by DFT of appropriately transformed data.