A fitting model based on the use of two independent blocks resulting from distributions of a hyperfine field and of one sextet of lorentzian lines is discussed for Mössbauer spectra recorded for Fe(Cu)MB nanocrystalline alloys. One distributed subspectrum is ascribed to the amorphous residual matrix, while the other independent block, from the hyperfine-field distribution, is attributed to Fe atoms located in the so-called interface zone. This region comprises atoms of nanocrystalline-grain surfaces and also atoms originating from the amorphous precursor, in close contact with the nanocrystalline grains. A sextet of lorentzian lines is attributed to the crystalline grains that have emerged from the amorphous alloy, which are unambiguously identified as phase. The distribution with low hyperfine fields can be eventually analysed in terms of two components accounting for the coexistence of electric and magnetic hyperfine interactions. In such an analysis, distributions of both quadrupolar splittings and hyperfine magnetic fields are employed. Examples of the present fitting model are provided for Mössbauer spectra of FeCuMB ( M= Zr, Ti, and NbCr) nanocrystalline alloys in the first stage of crystallization. The spectra have been recorded under various experimental conditions comprising low (77 K) and high (373 K) temperatures as well as an external magnetic field. More detailed discussion about the consequences of this novel fitting procedure with respect to the topography of hyperfine interactions within Fe-based nanocrystalline alloys is reported in part II, the following paper.