Among sections suspended were those giving power to the National Intelligence Service to carry out special operations on terror suspects and punishments for media houses for publishing materials deemed to be either encouraging or inducing terror attacks.
Other clauses are the one giving police the power to detain terror suspects for up to a year and the one limiting the number of refugees in the country.
The coalition is challenging the implementation of the controversial security laws which were passed during chaotic scenes in the National Assembly last December.
READ: 5 judges to hear CORD security laws petition from Jan 28
They are represented by nine lawyers including Orengo, Paul Mwangi, Haroun Ndubi, Anthony Oluoch, Celestine Opiyo, Norman Magaya, Faith Wanja and Stephen Kaluma.
The three-day hearing will take over a period of 15 hours.