  In this paper we consider the non-variational system $$
  \begin{cases}
  -\Delta u_i = \sum\limits_{j=1}^k a_{ij} u_j^{(N+2)/(N-2)}
  &\text{in }\mathbb R^N,\newline
  u_i>0 &\text{in }\mathbb R^N,\newline
  u_i\in D^{1,2}(\mathbb R^N).
  \end{cases} $$ and we give some sufficient conditions on the matrix
$(a_{ij})_{i,j=1,\dotsc ,k}$ which ensure the existence of solutions
bifurcating from the bubble of the critical Sobolev equation.
