Union City police today were investigating the death of Hector Diaz, 40, who was described as being active in anti-Castro Cuban nationalist movements.

The dead man was found lying on the floor of his home at 139 36th St. by his father, Juan. Police indicated he may have been dead for up to 12 hours.

Police also indicated that some literature and posters on Cuban politics were found in the dead man's apartment.

Police Chief Herman Bolte and Sgt. Henry Naumann, who has been placed in charge of the follow-up investigation, apparently will check out reports that Diaz feared for his life ever since the shooting deaths of two anti-Castro Cubans in April.