The pair are expected to arrive on Earth on Thursday or Friday, which could make the northern lights visible to some people, from Northern England to New York.
Here's what we know:
What is it?
As the two CMEs head towards Earth, they could cannibalise each other to become an even more powerful blast. This can happen when one CME is thrown out of the Sun and followed by a faster blast that consumes it.
The Space Weather Prediction Center (SWPC), part of the United States' National Oceanic and Atmospheric Administration (NOAA), has issued a geomagnetic storm warning for August 17-19, with a possible "strong" geomagnetic storm on Thursday.
The SWPC said: "Geomagnetic responses are likely to escalate to G3 (strong) conditions on August 18 due to the arrival at or near Earth of multiple coronal mass ejections that have departed the Sun since August 14.
"Despite the numerous CMEs, most are expected to have little to no impact at Earth, however, at least four have potential Earth-directed components."
It could result in aurora or northern lights being visible far further south than usual.
\u201cAURORA FORECAST: Tonight's aurora forecast for the potentially impending moderate/strong geomagnetic storm shows generally cloudy conditions over the Northeast and better than average conditions for parts of Michigan, the Rocky Mountain West, the Pacific Northwest. Details below:\u201d
— Space Weather Watch (@Space Weather Watch)
Should we be concerned?
The effects on Earth are likely to be very mild.
At worst, however, the solar storm could cause minor issues for some power systems, satellite impacts, and navigation systems problems.
Space weather expert Dr Tamitha Skov said: "The next five machine-gun solar storms to hit begins on the 18, according to NOAA/SWPC predictions.
"Expect sporadic aurora down to mid-latitudes through August 20. Disruptions to amateur radio expected on Earth's nightside. GPS reception issues at dawn, dusk & near aurora."
What has The Met Office said?
The Met Office said: "The auroral oval is likely to become enhanced on August 17 due to the combined effects of coronal hole fast wind and CME influences.
"Aurora could be visible as far south as northern England and in places of similar latitude, during the 17 and into the 18."
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