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A variable fiber-optic delay line (VFODL) is introduced that, to the best of the authors' knowledge, is the first time that a hybrid analog-digital VFODL is proposed to solve the dilemma of efficiently enabling many settable and long-duration time delays together with continuous and short time delays. In essence, this VFODL can provide near-continuous high-resolution time generation across an entire long-time-delay band. The VFODL is based on the concept of cascaded wavelength-sensitive and wavelength-insensitive time delays. A proof-of-concept VFODL built demonstrates near-continuous 0.5-ps-resolution time-delay control across an entire 25.6-ns time-delay band generating a total of 51 200 measurable time-delay bins. The experimental VFODL also gives a 4.95-dB total optical loss and a 1-ms time-delay control-setting speed. The proposed VFODL can be used in applications such as radio frequency photonic signal processing and radar testing.