Continued Fractions Associated with $\SL_3 (\mathbf{Z})$ and Units in Complex Cubic Fields Continued fractions associated with $\GL_3 (\mathbf{Z})$ are introduced and applied to find fundamental units in a two-parameter family of complex cubic fields. Keywords:fundamental units, continued fractions, diophantine approximation, symmetric spaceCategories:11R27, 11J70, 11J13