An optical linear feedback circuit has an optical loop delay path (10) for recirculating a sequence of optical signals, and an output path for outputting delayed optical signals after circulating one or more times around the loop. A selector (50) is provided for selecting one or more of the delayed optical signals from the sequence, and an optical logic circuit (20) is coupled to carry out a logical operation on the selected delayed optical signals to create an optical feedback signal which is coupled to the optical loop delay path, so that the optical feedback signal can be added to the sequence of optical signals already circulating. By recirculating around a loop, each round trip can be regarded as equivalent to a shift of a shift register, so longer sequences can be built up without needing an additional storage cell for each shift function.