Five general cargoships have been grounded by a storm off typhoon on Thursday.
All 66 crew on the vessels were safe on board near Kaohsiung, TVBS News reported.
Coast guard helicopters were on standby for an evacuation if needed.
Salvage work was not due to start until the weather improved.
The 4,900-dwt Tai Cang Hu 1 (built 1997) and the 5,000-dwt An Li 669 (built 2005) grounded south of the port approach.