Subjects made smooth pursuit eye movements with a target moving horizontally at 15 deg/sec. At a specified location the target either: (1) suddenly vanished; or (2) jumped to the fovea with target retinal velocity and feedback becoming 0 (target stabilized at the fovea). In each type of trial, the subjects either: “looked” at the target, “pushed” the target, or “passively” gazed. When the target vanished, eye velocity decreased exponentially with a short time-constant (τ ≈ 0.10 sec), regardless of whether the subjects were “looking,” “pushing” or “passively” gazing. However, some subjects while “pushing” (using an imaginary target) did generate low velocity smooth movement (1–2.5 deg/sec) late in the offset. When the target was stabilized at the fovea, eye velocity also decreased, but with a relatively long time-constant (τ = 0.4–0.8 sec). The time-constant was the same with both “looking,” and “pushing”, but was shorter for some subjects with “passive” gazing (τ = 0.1–0.5 sec). These findings show that smooth pursuit offset is influenced by the presence of a target, but is relatively independent of attentional mode. All of the pursuit offset responses can be simulated using a model of the pursuit system with target velocity and position inputs, and an internal positive feedback loop enabled by target presence.