The investigation centred around allegations in former Labour leadership contender Angela Eagle's constituency.
Ms Eagle faced criticism from sections of her party when she challenged Jeremy Corbyn in July 2016.
Wallasey Constituency Labour Party (CLP) remains suspended until the inquiry is finished in March.
Labour Party spokeswoman said further details of the two individuals' cases which have concluded will not be made available until next month.
A window at the MP's office building  in Wallasey was smashed at the time.
The Labour spokeswoman added: "The National Executive Committee will consider allegations against individuals and the CLP remains suspended while these allegations are investigated.
"The Labour Party has concluded investigations into two individual members. Other investigations remain ongoing."
Ms Eagle eventually withdrew her candidacy in favour of colleague Owen Smith, who was beaten by Mr Corbyn in the leadership poll.
Correction: An earlier version of this article stated an individual had been cleared of allegations of bullying and intimidation as part of the investigation. This has now been amended in light of clarification from the Labour Party.
Investigations into two members of a Merseyside Labour Party group accused of bullying and intimidation have now concluded, the Labour Party has said.