In nickel‐iron films thicker than about 100 nm (1000 Å), fast‐rising field pulses along the hard anisotropy axis lead to a new kind of wall displacement called ``wall streaming,'' which does not require any field component parallel to the wall necessary for all other wall motion processes. The walls are displaced with a very regular wall step width per pulse which strongly depends on the strength of the pulse field and on the pulse rise and fall times, but not on the pulse duration. The direction of wall motion reverses if the pulse polarity is reversed. During the application of a sequence of uniform pulses, the direction of wall motion may also reverse, beginning at one end of the wall, with a reversing line (interpreted as being a Ne´el line moving along the wall. The phenomenon is explained as a consequence of the gyromagnetic behavior of the magnetization in the Bloch walls. A detailed theory is presented, in which the intrinsic spin damping and the film inhomogeneity (characterizable by the coercivity) are to be taken into account. Wall streaming may contribute to a destruction of the information stored in magnetic films thicker than 100 nm (e.g., in plated‐wire memories) as soon as fast‐rising (tr≲20 nsec) pulses are applied.