adverb, adverb taking the 'to' particle
moment by moment; hour by hour; with each passing moment
Describes a situation that changes or progresses continuously as time passes, often with a sense of urgency or inevitability. Commonly used with と (刻一刻と).
刻一刻と締め切りが迫っている。
The deadline is approaching moment by moment.
状況は刻一刻と変化している。
The situation is changing with each passing moment.