[en] The effect of axial asymmetry of the magnetic field on transverse plasma losses from traps with improved longitudinal confinement is discussed in this paper. The role of these losses is characterized by the angle of rotation Δpsi of the guiding centre of the particle around the magnetic axis during motion of the particle from mirror to mirror. The transport regimes are classified as a function of the angle Δpsi. Corresponding analytical estimates of the transport coefficients are presented. - A stochastic instability leading to collisionless diffusion due to field perturbation as a result of slight misalignments in the magnetic system was studied experimentally in terms of a specially constructed electron model in which the electrons moved in longitudinal magnetic and radial electric fields. - Resonance and stochastic diffusion were also investigated numerically in terms of a special model. The numerical results are in satisfactory agreement with simple analytical estimates for the instability boundary and diffusion rate under the joint effects of resonances and multiple scattering. (author)