  Let X be a finite type simply connected rationally elliptic CW-complex with
Sullivan minimal model $(\Lambda V, d)$ and let $k \geq 2$ the biggest integer
such that $d=\sum \limits_{\underset{}{i\geq k}}d_i$ with $d_i(V) \subseteq
\Lambda^iV$.
  In \cite{murillo02} the authors showed that if $(\Lambda V,d_k)$ is morever
elliptic then $cat(\Lambda V,d)=(k-2)dimV^{even} + dimV^{odd}.$
  Our work focuses on the estimation of L.S.-category of such spaces in the
case when $k=3$ and when $(\Lambda V,d_3)$ is not necessarily elliptic.
