Memory for the initial position of a moving target may be displaced forward in the direction of target motion (referred to as a Fröhlich Effect, e.g., Müsseler & Aschersleben, 1998) or displaced backward in the direction opposite to target motion (referred to as an Onset Repulsion Effect, e.g., Thornton, in press). There are important methodological differences between studies reporting a Fröhlich Effect and studies reporting an Onset Repulsion Effect (e.g., a Fröhlich Effect is typically found with faster velocities and when the target appears to emerge into a window, whereas an Onset Repulsion Effect is typically found with slower velocities and when the target is presented in isolation). In the current experiments, a computer-animated horizontally or vertically moving target was presented, and after the target vanished, observers indicated the remembered initial position or remembered final position of the target. Experiments 1 and 2 extended previous studies (Hubbard & Motes, 2002) in which an Onset Repulsion Effect was exhibited with slow velocities; Experiment 1 presented much faster velocities, and Experiment 2 added an surrounding window adjacent to the trailing edge of the target's initial position and leading edge of the target's final position. Whether a Fröhlich effect or Onset Repulsion Effect is exhibited may also reflect dynamic aspects of memory, and so Experiment 3 varied whether observers indicated remembered initial position before or after indicating remembered final position. Overall, results suggest a Fröhlich Effect is more likely when the target emerges into a window and an Onset Repulsion effect is more likely when the target is presented in isolation. Velocity per se did not influence whether a Fröhlich Effect or an Onset Repulsion Effect was exhibited. The relationship of displacements in memory for starting point to displacements in memory for final point (i.e., to representational momentum, e.g., Hubbard, 1995) is also discussed.