The first, which took place around 5am, is described as a serious police incident. This led to the closure of the eastbound lane between Junctions 29 and 30.
The second incident, an accident between J24 and J25 westwards near Newport, took place around 08:00. This resulted in the road being closed and traffic being diverted from the J24 access slip.
Officers closed the eastbound lane between J24 and J26.
South Wales police said in a Twitter post this morning that they were “currently engaging in a serious incident on the M4 at junction 30 eastwards”.
The force added: “The road will be closed until further notice, we will recommend that alternative routes be used.
“Thank you for your patience and understanding.”
A Welsh Ambulance Service spokesman said: “We were called earlier today after an incident near junction 30 of the M4, with several resources sent to the scene.”
Of the 08:00 incident, Traffic Wales South said on Twitter: “# M4 travel West between J24 Coldra to J25 Caerleon – Road closed.
“# M4 travel East between J26 Malpas and J24 Coldra – Road closed.
“Emergency services are on the scene.
“Please avoid the area.”