A South Texas man accused of beheading his common-law wife's three children was found guilty of capital murder Monday at his second trial.

A state appeals court had overturned John Allen Rubio's previous conviction and death sentence in 2007, saying the children's mother had wrongly been allowed to testify. A second jury deliberated for about three hours before convicting him again.

Rubio, 29, of Brownsville, had pleaded not guilty by reason of insanity, and his defense attorneys had argued that the sheer brutality of the crime showed he was not in his right mind. Defense attorney Nat Perez described it during his closing argument as "overkill."

Evidence showed Rubio made increasingly ferocious attempts to kill the children, strangling and stabbing them, then finally cutting off their heads. Rubio initially said he killed the children, all under age 4, because they were possessed.

Police discovered the bodies of 3-year-old Julissa Quesada, 14-month-old John E. Rubio and 2-month-old Mary Jane Rubio on March 11, 2003, in a squalid Brownsville apartment.

Rubio was convicted on four counts of capital murder. Each death was covered by one count, and the fourth count included all of them.

The trial will now move to a punishment phase, in which prosecutors plan to again seek the death penalty.