Self-organisation of phase-space structures is ubiquitous in collisionless (or Vlasov) plasmas. Here we focus on 1D electron-ion plasmas with periodic boundary conditions. The phase-space (PS) of particle trajectories in that case is composed of position x and velocity v. In this context, BGK-like islands in PS with a local deficit of particles, called as a phase-space holes (PS holes) form spontaneously in a range of velocities where ion and electron distribution function have velocity gradients of opposite signs. Growth and acceleration are closely linked to the equilibrium velocity gradient via the Liouville conservation of phase-space density. The aim of this research is to develop the theory of PS hole growth and acceleration. The Vlasov-Poisson system is solved numerically with the semi-Lagrangian code COBBLES [1]. For each simulation, the initial condition includes a single electron PS hole with prescribed dimensions and shape, which satisfy a non-linear dispersion relation [2]. The measured instantaneous nonlinear growthrate of the PS hole are in qualitative agreement with analytical theory, which assumes constant equilibrium velocity gradients in the velocity region spanned by the hole [3, 4]. To improve the validity range of this theory, we account for the variations of velocity gradients, which are in fact significant. Further, based on a similar procedure, but in the context of a gyro-bounce-averaged model [5], we calculate an analytic expression for the nonlinear growth-rate of a PS hole in trapped-particle-driven drift-wave turbulence. References [1] M. Lesur, Y. Idomura, X. Garbet, Phys. Plasmas 16, 092305 (2009) [2] H. Schamel, Plasma Phys. 14, 905 (1972) [3] T. H. Dupree, Phys. Fluids 26, 2460 (1983) [4] D. J. Tetreault, Phys. Fluids 26, 3247 (1983) [5] M. Lesur, et al., Phys. Plasmas 24, 012511 (2017)