  In recent studies, new measures of complexity for nonlinear systems have been
proposed based on probabilistic grounds, as the LMC measure (Phys. Lett. A {\bf
209} (1995) 321) or the SDL measure (Phys. Rev. E {\bf 59}
  (1999) 2). All these measures share an intuitive consideration: complexity
seems to emerge in nature close to instability points, as for example the phase
transition points characteristic of critical phenomena. Here we discuss these
measures and their reliability for detecting complexity close to critical
points in complex systems composed of many interacting units. Both a
two-dimensional spatially extended problem (the 2D Ising model) and a
$\infty$-dimensional (random graph) model (random Boolean networks) are
analysed. It is shown that the LMC and the SDL measures can be easily
generalized to extended systems but fails to detect real complexity.
