"The decline will be due largely to rising competition in emerging markets, where lower-priced handset models from local competitors should continue to gain market share at the expense of the big two," the ratings agency said in a statement.
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"In these markets, where cost is relatively more important than global brand strength or cutting-edge technology, competitors' devices retailing at $100-$300 can offer most of the key features of more expensive phones from Samsung and Apple."
iPhone 6 'not revolutionary'
The big two companies' combined smartphone shipment volume will "stagnate" at around 450 million to 460 million units in 2014, down from 467 million in 2013, despite the global market expected to rise by around 20 percent to 1.2 billion, Fitch said.
Both Apple and Samsung are betting on new products to maintain dominance in mobile device market.
Apple is widely expected to release the iPhone 6 in September, while Samsung is rumoured to unveil another smartwatch in its Galaxy Gear range.
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But Fitch said that this would not be enough to save the technology giants' eroding dominance.
"Apple's next iPhone…is likely to have a larger screen, and developments are likely to be incremental rather than revolutionary. We believe that the innovations - which include curved screens and compatible wearable devices - are unlikely to change the trend facing Samsung and Apple," Fitch said.