When magnetic cores with a square hysteresis loop are used for a time delay Crcuit or a pulse counter circuit, and if these circuits are designed by the use of the static hysteresis loop, the ac magnetization curve, or the control magnetization curve (CMC) which is the basic characteristic of a magnetic amplifier, there is apt to be a marked discrepancy between their design values and measured values. Since, in the flux control of magnetic cores used for a time delay circuit or a pulse counter circuit, the flux, contrary to the case with a magnetic amplifier, arrives at the negative saturation from the positive saturation by many intermittent signal voltages, a new characteristic quite different from CMC and other characteristics must be adopted as the standard of the design in this case. It was for this reason that instantaneous relation between the rate of flux change and the exciting current was examined in the case in which real flux resetting behaviors of a time delay circuit or a pulse counter circuit were taken into consideration, by using grain-oriented 50 per cent permalloy as the sample, with a view to obtaining core characteristics serviceable enough for exact design methods of a time delay circuit or a pulse counter circuit. Various useful results have been obtained as to: 1) how the correlation between rate of flux change and instantaneous values of exciting current icchanges in proportion to the flux values, 2) how the amount of reset flux will change according to the flux value and the rate of flux change , and 3) how the above-mentioned relations are connected to the tape thickness of the magnetic core. This paper reports the results of this investigation.