  We analyze the possibility of description of D-dimensional massless particles
by the Lagrangians linear on world-line curvatures k_i,
  {\cal S}=\sum_{i=1}^Nc_i\int k_i d{\tilde s}.
  We show, that the nontrivial classical solutions of this model are given by
space-like curves with zero 2N-th curvature for N\leq[(D-2)/2]. Massless
spinning particles correspond to the curves with constant k_{N+a}/k_{N-a}
ratio.
  It is shown that only the system with action {\cal S}=c\int k_N d{\tilde s}
leads to irreducible representation of Poincar\'e group. This system has
maximally possible number (N+1) of gauge degrees of freedom. Its classical
solutions obey the conditions k_{N+a}=k_{N-a}, a=1,..., N-1, while first N
curvatures k_i remain arbitrary. This solution is specified by coinciding N
weights of the massless representation of little Lorentz group, while the
remaining weights vanish.
