Tie linear electrostatic stability of a low$ collisionless plasma in a magnetic field B = @, , is studied. We consider distribution functions of the type:The Laplace-Fourier transform of the electric potential is a meromorphic function whose poles in Fourier space are given by:where the functional D is a convergent infinite continued fraction.Kz(n'/,J-ll), which are left aside in the usual local theories.The above dispersion relation permits us to study the two wavelength ranges (lKzv~&,\ 2 1 and