"In our fight against match-fixing we have got to a stage that our Anti-Corruption Unit (ACU) chief Lord Paul Condon can say to us that he believed that the problem of match-fixing is under control but it's not gone forever," said Speed.
"If we go back to 2000, cricket had a very serious problem with corruption when we saw then a number of captains and other players were implicated. We had to deal with that problem," Speed, an Australian, said after an international seminar on cricket.
"We know that allegations come up and we are vigilant."
The ICC was forced to a form the unit after late South African captain Hansie Cronje confessed to taking money from bookmakers in June 2000.
Former Indian captain Mohammed Azharuddin and ex-Pakistani skipper Salim Malik were also banned for life after inquiries in their respective countries.
"ICC spends in excess of one million pounds on anti-corruption and security unit and we will continue to do that because we believe that it is one of the most serious problems that has confronted cricket," said Speed.
Pakistan banned for life Malik and pacer Ataur Rehman and imposed fines on Wasim Akram, Waqar Younis, current captain Inzamam-ul-Haq, Saeed Anwar, Mushtaq Ahmed and Akram Raza after an inquiry by Justice Malik Mohammad Qayyum in 1998-1999.
A second inquiry conducted by Justice Karamat Bhandari in 1999-2000 into two match-fixing allegations in the 1999 World Cup held in England cleared all players.
Speed expressed satisfaction with both the inquiries.