Both died over the weekend
34 year old Carl Walters died in custody on Saturday and 64 year old Anthony Newman died on Sunday.
A spokesman said: "As with all deaths in custody, there will be an independent investigation by the Prisons and Probation Ombudsman."
Yesterday (Wednesday 3rd April) the prison was named as one of three to undergo new inspections.
Independent Reviews of Progress (IRPs) will give Ministers an independent assessment of progress made in implementing recommendations after concerning inspections.
Last year serious concerns were raised about HMP Exeter after an inspection, which lead to urgent intervention from the Secretary of State.
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Work begins on project to rebuild fire-hit Exeter landmark
Car crashes through wall near Exeter Cathedral
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Naming streets after famous people could be over in parts of Devon
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