In this paper we extend the notion of Poisson scale-space. We propose a generalisation inspired by the linear parabolic pseudodifferential operator $\sqrt{-\Delta+m^2}-m$, 0≤m, connected with models of relativistic kinetic energy from quantum mechanics. This leads to a new family of operators $\{Q^m_t\,|\,0\leq m,t\}$ which we call relativistic scale-spaces. They provide us with a continuous transition from the Poisson scale-space {Pt | t≥0} (for m=0) to the identity operator I (for $m \longrightarrow +\infty$). For any fixed t0>0 the family $\{Q_{t_0}^m~|~ m\geq 0\}$ constitutes a scale-space connecting I and $P_{t_0}$. In contrast to the α-scale-spaces the integral kernels for $Q^m_t$ can be given in explicit form for any m,t≥0 enabling us to make precise statements about smoothness and boundary behaviour of the solutions. Numerical experiments on 1D and 2D data demonstrate the potential of the new scale-space setting.