The Boltzmann equation is solved to obtain a two-dimensional electron distr
ibution function (2D EDF) to investigate the relaxation of highly anisotrop
ic EDFs in plasmas acted by a strong laser field. Two kinds of anisotropic
EDFs are considered: (i) elongated along the external field polarization di
rection, and (ii) elongated perpendicularly to it. Two kinds of external fi
elds are considered: (i) a linearly polarized field with constant amplitude
, and (ii) a linearly polarized ultrashort-pulsed field. Basic results of t
he calculations are (i) the EDFs initially elongated perpendicularly to the
laser field polarization relax considerably faster than EDF's elongated al
ong the field polarization; (ii) an initially highly anisotropic EDF, of an
y shape, in a strong field relaxes slower than in a weak field, or in absen
ce of any field; (iii) in cases of fast relaxation, an EDF initially elonga
ted perpendicularly to field polarization approaches isotropization after h
aving acquired a shape elongated parallel to the field polarization; (iv) d
uring its relaxation, the calculated EDF is approximated rather well by a b
i-Maxwellian with the same effective temperatures.