In the NHK Cup, starting at the beginning of the game, players have 30 seconds to make each move, but have 10 extended thinking periods (kouryo jikan=考慮時間) of one minute. (For those interested in "real-world" implementations of time systems, the above is essentially a word-for-word translation of how the time system is described at the beginning of each program.)
And for those interested in arcane variations of byo-yomi conventions, and IIRC, the seconds are read off at the 10, 20, 25, and 28 second point of each thirty-second period, and the 30, 40, 50, 55, 58 second point of each extended thinking period. However, after all ten extended thinking periods have been exhausted, the last ten seconds are read off one by one: ichi, ni, san, with the player in question losing when the byo-yomi-gakari pronounces the dreaded "juu".
(not sure if the description "one period of" is correct without the "per move" qualifier, as 30 second periods are given to each move for as many moves as there may be in a game.)