Broadband records of weak local earthquakes occasionally exhibit long-period, pulselike signals, appearing exclusively on horizontal components. Such signals have been recorded at station Sergoula in the Corinth Gulf by Guralp CMG-3T (100-sec) and Wielandt-Streckeisen STS-2 (120-sec) instruments. The pulses can be perfectly matched by the instrumental responses to a small step of acceleration. Similar pulses, observed during moderate near earthquakes at stations of the Greek National Network equipped with Lennartz Le-3D/20s (20-sec) sensors, can be explained in the same way. Numerical simulation of the pulses allows their removal, thus making the records fully utilizable for waveform inversion in seismic source studies. Prerequisite for that is precise knowledge of the instrument transfer function. We found that poles and zeros of the CMG-3T and STS-2 sensors were consistent with those given by the manufacturer, whereas those of the LE-3D/20s were not. We identified the latter by inversion of spontaneous pulses incidentally appearing in LE-3D/20s records without relation to any earthquake. What actually generates the earthquake-related horizontal acceleration steps remains unclear. Rapid and permanently lasting tilt is a very likely candidate. When we numerically model a coseismic near-field static displacement, we actually find a tilt step, but its amplitude is several orders below the observed values. We therefore rather speculate that it is a very local tilt, triggered by high-frequency ground vibrations.