Moment by moment; from hour to hour; continuously changing with each passing moment (often implying urgency).
事故現場の状況は一刻一刻変わっている。救助が急がれる。
The situation at the accident scene is changing by the moment. Rescue is urgent.
薬の投与は一刻一刻を争うため、速やかに処置した。
Because medication administration was a race against time, we treated him promptly.
時計の針は一刻一刻と進んでいく。
The hands of the clock move forward moment by moment.