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Massless spinning particle and tensionless string models on $AdS_d$background in the projective-space realization are proposed as constrainedHamiltonian systems. Various forms of particle and string Lagrangians arederived and classical mechanics is studied including the Lax-typerepresentation of the equations of motion. After that transition to the quantumtheory is discussed. Analysis of potential anomalies in the tensionless stringmodel necessitates introduction of ghosts and BRST charge. It is shown thatquantum BRST charge is nilpotent for any $d$ if coordinate-momentum orderingfor the phase-space bosonic variables, Weyl ordering for the fermions and $cb$($\gamma\beta$) ordering for ghosts is chosen, while conformalreparametrizations and space-time dilatations turn out to be anomalous for theordering in terms of positive and negative Fourier modes of the phase-spacevariables and ghosts.

Massless spinning particle and null-string on $AdS_d$: projective-space approach