The first investigation looks at whether Qualcomm, which is the market leader for baseband chipsets, offered cash to customers if they bought exclusively or almost exclusively baseband chipsets from it.
The second investigation will look into whether Qualcomm engaged in 'predatory pricing' by charging prices below costs with a view to forcing its competition out of the market.
European Competition Commissioner Margrethe Vestager said: "Many customers use electronic devices such as a mobile phone or a tablet and we want to ensure that they ultimately get value for money."
It would be jolly good if the EU started investigating if consumers were getting their money's worth. Looking at the mark-up on some mobile gadgets we would have thought a bigger inquiry was a long time in coming.