Muldoon is a town in southwestern Fayette County, Texas, United States, located 10 miles north of Flatonia and 16 miles southwest of La Grange. Its population, according to the 2010 census, is 114 and is growing very slowly. It is on the junction of FM 154 and FM 2237.The town of Muldoon was named after Father Michael Muldoon, a clergyman who briefly served Stephen F. Austin's first colonists. He was the only non-Hispanic member of the Monterrey, Mexico Diocese and was probably assigned his duties because he spoke English. He was born in County Cavan in Ireland and later ordained in Spain.In 1834, Muldoon travelled to Mexico to visit Stephen F. Austin during Austin's confinement there. Later, he assisted William Wharton in his escape from a Matamoros prison in 1837, after which the town of Wharton, Texas was founded. Muldoon was openly pro-Texan, which led to his own brief imprisonment by the Mexican government.