The Accra Police command has arrested two Nigerians who joined Thursday's demonstration in Accra.
The police say the demonstration was meant for Ghanaians and Ghanaians alone.
"It was not for other nationals to join," Joseph Obenefo Darkwa of the police CID told Joy News.
The two held the Nigerian flag side-by-side right in the belly of the demonstrators, singing their own songs and chanting.
One of them told Myjoyonline.com right in the middle of the demonstration that: "We are comrades from Nigeria. We are protesting fuel prices hikes. We have undergone similar things in Nigeria around January. We believe in a united Africa. Nigeria and Ghanaians we are brothers. Whatever affects Ghanaians affect Nigerians. So we are here in solidarity with Ghana."
But it appears the police are not convinced by his explanation, however innocent it sounded.
Joseph Obenefo Darkwa said the conduct of the two was "offensive."
Ahead of the Thursday's demonstration security expert at the Kofi Annan International Peacekeeping Centre Dr Kwasi Aning had hinted of the possibility of the demonstration being infiltrated by fifth columnist or elements to foment trouble.
It is however too soon to conclude the two arrested Nigerian have any such ulterior motives
Joseph Obenefo Darkwa said the police have begun profiling the two gentlemen and are investigating their conduct.
Meanwhile the police say the demonstration was highly successful.
Police Public Affairs Director DSP Cephas Arthur said they were professional in the dealings with the demonstrators, but was quick to express his disappointment with the decision by the demonstrators to abort an initial plan to converge at the Hearts park and instead chose the Independence Square.