In this note we propose a method to classify homogeneous nilpotent elements
in a real $Z_m$-graded semisimple Lie algebra $g$. Using this we describe the
structure of the orbit space of homogeneous elements in a real $Z_2$-graded
semisimple Lie algebra. A classification of 4-vectors (resp. 4-forms) on $R^8$
can be given using this method. Thus the $SL(R^ 8)$-orbit space of $k$-vectors
(resp. $k$-forms) on $R ^ 8$ can be completely analyzed.