Samuels and Shillingford were reported at the end of the second day's play Friday by on-field umpires Richard Kettleborough and Nigel Llong, TV umpire Vineet Kulkarni and Andy Pycroft of the Emirates Elite Panel of ICC Match Referees, an International Cricket Council (ICC) statement said.
Pycroft handed over the copies of the reports to the West Indies team manager after the conclusion of the Test.
"The umpires' reports have cited concerns over the two bowlers' bowling actions, with particular references to Samuels' 'quicker deliveries' and Shillingford's 'doosras'," the ICC said.
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Samuels' and Shillingford's bowling actions will now be scrutinised further under the ICC process relating to bowlers reported in Tests, ODIs and T20Is.
As per Clause 2.2 of the ICC regulations, the players are required to submit to an independent analysis of their bowling actions within 21 days. The assessment reports have to be sent to the ICC within another 14 days.
If the allegations are proved to be true during the independent analysis, the players would be suspended from bowling in international cricket. However, until the independent assessments are received, the players would be permitted to continue bowling.
The duo was previously reported and suspended from bowling in international cricket after their their actions were found to be illegal.
They were, however, allowed to resume bowling after they underwent remedial work on their actions and further testing.
Samuels was reported in February 2008 and resumed bowling in international cricket in September 2011. Shillingford was reported November 2010 and restarted bowling June 2011.