The concept of a traveling-wave free-electron laser (TWFEL) is presented. This hybrid device consists of both a periodic waveguide and a planar wiggler. It combines the interaction mechanisms of both the traveling-wave tube (TWT) and the free-electron laser. This combination produces a synergistic interaction. A linear model of the TWFEL is derived in this paper. It results in a general dispersion equation for the TWFEL interaction. Coupling coefficients are derived for various ratios between the wiggler period W and the periodic waveguide period p. It is shown that when W=p the parametric interaction is composed of a double FEL interaction, a TWT interaction, and a hybrid interaction. All these are in resonance with three different spatial harmonics. The coupling coefficient for this scheme is a complex sum of the known FEL and TWT terms, and of complex terms for their cross coupling. It is shown that the coupling coefficient of the synergistic TWFEL interaction (and consequently its gain) can be larger than the sum of the two separate interactions. Simpler TWFEL schemes in which W p (single-harmonic interaction) and W=2p (two-harmonic interaction) are presented first as an introduction for the analysis of the W= TWFEL interaction. A compact TWFEL based on a miniature wiggler, which functions also as a periodic waveguide, is proposed for operation in the millimeter-wave range with a tenuous low-energy e beam.