  This is part one of our study of models of jets with distributed electron
acceleration. We present here our assumptions, basic equations, and their
solutions for the steady-state electron distribution. We assume the shape of
the rate of electron acceleration and the dependencies of its normalization and
the magnetic field strength on the height along the jet. Our focus is on the
hard spectral state of black-hole binaries, for which we take into account that
their typical radio spectra are flat. This appears to require a constant
dissipation rate per unit logarithmic length and conservation of the magnetic
energy flux. Our electron kinetic equation includes adiabatic and radiative
losses and advection, and our photon radiative transfer equation includes
synchrotron absorption and emission and Compton emission. Apart from the
self-Compton process, we take into account Compton scattering of stellar and
accretion photons and absorption of very-high energy gamma-rays by pair
production on soft photons. We present a general solution of the kinetic
equation with advection and radiative and adiabatic losses and an analytic
solution in the case of dominant synchrotron losses in conical jets. In the
following paper, we present detailed spectra resulting from our equations as
applied to Cyg X-1.
