Andreas Von Knorre and Elton Hinz, both 21, were charged at a district court with committing trespass and vandalism in the early hours of November 8th.
Both men appeared relaxed as the charges were read to them in German by an interpreter.
Prosecutors told the judge the two men will be remanded in police custody until "to assist investigations and re enact the crime scene".
The charge sheets said Van Knorre and Hinz broke into the suburban depot and spray-painted graffiti on the exterior of a metro train cabin. The depot is a restricted zone surrounded by fences topped with barbed wire.
The two men were extradited by neighbouring Malaysia after being apprehended at Kuala Lumpur International Airport as they were leaving for Australia.
The Straits Times newspaper said in a report the two men have visas to work in Australia.
For trespassing they face up to two years in jail, a fine of up to Sg$1,000 ($800), or both.
For vandalism, they face up to three years in jail or a fine of up to Sg$2,000, and between three and eight strokes of a rattan cane — a punishment dating back to British colonial rule.
Singapore, a leading Asian financial hub, is well-known for its tough stance on crime.
The city-state's vandalism laws became global news in 1994 when an American teenager, Michael Fay, was caned for damaging cars and public property despite appeals for clemency from the US government.
In 2010, Swiss expatriate Oliver Fricker was sentenced to seven months in jail and three strokes of the cane for vandalising a train at a depot in the city-state.
Caning entails being whipped with a rattan stick on the back of the thigh below the buttocks, which can split the skin and leave lasting scars.