An analog-to-digital conversion circuit, in which the coarse bits are produced by a counter (25), is made suitable for processing a video signal by having, in the event of fast large amplitude variations, an analog-to-digital converter (3), connected to the input (1) of the conversion circuit, write into the counter in response to a threshold-crossing signal produced by a difference threshold circuit (91, 93, 57), while slow and small amplitude variations are followed by a correction circuit (97, 113, 111, 119, 61, 63) coupled to an output (49) of a digital-to-analog converter (47) which is connected to the outputs of the conversion circuit, the correction circuit also being coupled to the input (1) of the conversion circuit, which correction circuit corrects the counting position, while the fine bits are obtained from a fine analog-to-digital converter (113, 97, 103, 105) which is responsive to the difference between the signal at the input (1) of the conversion circuit and the signal at the output (49) of the digital-to-analog converter (47).