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The cascaded soliton spectral tunneling (SST) effect is proposed and numerically investigated in multiple optical fiber segments, which work together to transfer the soliton pulse over a wide wavelength span. A triple-cladding fiber and a solid core step-index photonic crystal fiber are carefully studied and demonstrated to have three zero-dispersion wavelengths (ZDWs), which can evoke the SST effect individually and therefore are good candidates for the cascaded SST effect. Such a cascaded SST scenario can be applied to optical wavelength conversions, and the transferred wavelength could be flexible tuned by tailoring the position of ZDWs. Numerical simulations in both fiber segments are shown, and a soliton transfer over 570 nm is demonstrated with two fiber segments. Meanwhile, soliton pulse compression and supercontinuum generation are also observed to accompany each SST effect.