The incidents at Portiuncula Hospital took place in May and July this year.
A case of an infant losing oxygen to the brain, and a stillbirth, are being investigated by the HSE at Portiuncula Hospital.
The Irish Independent is reporting HSE Chief Executive Bernard Gloster will reveal details of the two incidents at a hearing of the Oireachtas Health Committee today.
In his statement he will say another incident of hypoxic-ischemic encephalopathy was recorded at the hospital in July.
While a stillbirth on the maternity ward in May is also being investigated bringing the total number of reviews to 12.
Women with complex pregnancies will be transferred to other maternity wards from next month, despite thousands protesting for the retention of full maternity services at the hospital in Ballinasloe last month.
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