Today the inquiry is set to hear from Donald Dunphy's brother, Dick Dunphy, as well as Dunphy's daughter's boyfriend, Billy Corcoran.
The discussion is expected to focus on Donald Dunphy’s character.
Dunphy was shot and killed in his Mitchell's Brook home on Easter Sunday, 2015, by RNC officer Joe Smyth, who was assessing a potential threat against the premier.
Earlier testimony at the inquiry has suggested there was some sort of falling-out and bitter family conflict between Donald Dunphy and Dick and Debbie Dunphy.
Justice Leo Barry, who is leading the inquiry, said Debbie Dunphy's doctor's note excusing her from testifying is pretty vague.
Barry said that there could be "significant adverse consequences" to anybody who is trying to get out of testimony without adequate reason.