  A system of nonlocal electron-transport equations for small perturbations in
a magnetized plasma is derived using the systematic closure procedure of V. Yu.
Bychenkov et al., Phys. Rev. Lett. 75, 4405 (1995). Solution to the linearized
kinetic equation with a Landau collision operator is obtained in the diffusive
approximation. The Fourier components of the longitudinal, oblique, and
transversal electron fluxes are found in an explicit form for quasistatic
conditions in terms of the generalized forces: the gradients of density and
temperature, and the electric field. The full set of nonlocal transport
coefficients is given and discussed. Nonlocality of transport enhances electron
fluxes across magnetic field above the values given by strongly collisional
local theory. Dispersion and damping of magnetohydrodynamic waves in weakly
collisional plasmas is discussed. Nonlocal transport theory is applied to the
problem of temperature relaxation across the magnetic field in a laser hot
spot.
