B757-200
Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Less Severe
Flight Crew Landed As Precaution; Flight Crew Returned To Departure Airport
Aircraft
After takeoff out of Airport ZZZZ passing 8000 FT on we received R ENG FIRE and FLAP red EICAS messages; followed shortly by L ENG FIRE.  Looked immediately to fire handles; they were not lit.  EGTs (Exhaust Gas Temperature) showed normal for both engines.  A host of EICAS messages suggested an electrical malfunction (additional messages included CABIN PRESSURE; MAIN CARGO DOOR; among others.)  CA [notified ATC] and we immediately returned to field.  Fire trucks met the aircraft and reported no sign of fire.Possible electrical or EICAS computer malfunction.
B757-200 First Officer reported multiple false alerts; including false engine fire warnings; from a probable EICAS malfunction.