the set of unstable vectors of a representation $v$ of a reductive group $g$, the so-called {\\it nullcone\\/} $n_v$, contains a lot of information about the geometry of the representation $v$. e.g. if $n_v$ contains finitely many orbits then this holds for every fiber of the quotient morphism $\\pi_v\\colon v \\to v/\\!\\!/ g$. the hilbert-mumford criterion allows to describe the nullcone as a union $\\bigcup g v_\\lambda$, using maximal unstable subspaces of $v_\\lambda \\subset v$ annihilated by a 1-parameter subgroup $\\lambda$ of $g$. they correspond to maximal unstable subsets of weights which allows some interesting combinatorics. we will give some methods how to determine the irreducible components $gv_\\lambda$ of the nullcone and will describe their behavior if one considers several copies of a given representation $v$. a rather complete picture is obtained for the so-called $\\theta$ representations studied by kostant-rallis and vinberg. e.g. we were able to show that for the 4-qubits $q_4:={\\bf c}^2\\otimes {\\bf c}^2\\otimes {\\bf c}^2 \\otimes {\\bf c}^2$ the nullcone has four irreducible components all of dimension 12 for one copy and 12 irreducible components for $k\\geq 2$ copies. these 12 components decompose into 3 orbits under the obvious action of $s_4$ on $q_4$, each one consisting of 4 elements, of dimensions $8k+4$, $8k+3$ and $8k+1$. (this is joint work with nolan wallach.)