Six Cuban detainees were continuing to refuse food at the Immigration Detention Centre on Friday (18 January.)
It comes as part of a hunger strike which began on Tuesday (15 January).
Initially, eight migrants started the hunger strike, but two have since started eating.
The group began their hunger strike following a peaceful protest last week, in response to issues like lack of access to free bilingual lawyers, the pace of Immigration processing and a wish to be released from detention.
The group arrived in Cayman in September last year, when their boat got into distress in local waters on the way to Central America.
The Prison Service said it was monitoring the situation as per protocols. Acting Chief Immigration Officer Garfield Wong has met with the migrants.