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Thousands of people sought emergency shelter as the two storms moved closer to land and caused rivers and streams to burst their banks.
"There is a lot of water and the rivers are full," said Luis Felipe Puente, national coordinator for Mexico's emergency services. "There will be yet more rain when the storms make landfall."
In Guerrero state on Mexico's Pacific coast, 11 people died in landslides and as buildings collapsed because of heavy rain on Saturday and Sunday. In the states of Puebla and Hidalgo, three people were killed when a wall collapsed and three people were carried away by a strong current.
On the Gulf coast, Hurricane Ingrid, a Category 1 storm with sustained winds of 120kmh, was drenching Tamaulipas and Veracruz states on Sunday, sending more than 6,000 people into emergency shelters.
Mexico's state oil monopoly Pemex, which has most of its installations in the Gulf, evacuated three platforms off the Tamaulipas coast on Sunday.
In Veracruz, there have been landslides and localized flooding, but no injuries or deaths reported, local emergency services officials said.
Ingrid, which was located 175km from Tampico, Veracruz at 2100 GMT, was expected to bring hurricane conditions to Veracruz and Tamaulipas early on Monday morning (local time) when the storm was forecast to reach land.
The storm could strengthen slightly before reaching land, the Miami-based National Hurricane Center (NHC) said.
On the Pacific coast, Tropical Storm Manuel was weakening after making landfall, but the risk of flash flooding and landslides continues, the NHC said.
Manuel had sustained winds of 75kmh and the storm was bringing high waves and between 25-38cm of rainfall to the area's beach resorts, including Acapulco.
Flooding that reached up to 1.5-2m in some places was affecting parts of Acapulco, Puente said.
Because of Ingrid, several towns in Tamaulipas canceled plans for independence celebrations on Sunday night, local media reported. Usually Mexicans flock to their town square to hear local officials give the call to arms known as "El Grito", an echo of Miguel Hidalgo's original call to arms against the Spanish in 1810.