Nobody knows exactly where he was planning to go, but the border guards at Gyor, 70 miles from Budapest and about the same distance from Vienna, were sure he was trying to cross illegally.
"I don't know why I am being held here, I am a tourist and I wanted to go to Vienna to see my aunt," he told them. But not many tourists try to cross Hungary's "green" border with Austria at 2am without any papers.
Rashid is one of thousands who are taking their chances on Europe's people-smuggling network, which stretches through Turkey and the former Soviet Union to the favourite destinations - Germany, Austria and, increasingly, Britain.
Between 600 and 800 Kosovo Albanians alone are caught every month on the Austro-Hungarian border.
People-smuggling networks, often linked to organised crime, use the Hungarian capital as their collection and distribution point, say officials. Hungary's proximity to the West, and the lack of visa requirements for citizens of countries such as Turkey, Yugoslavia and much of the former Soviet Union, has made Budapest the smugglers' favourite city.
Once an illegal immigrant has made it across into Austria, and the Schengen zone, he or she can link up with fellow-countrymen who will then pass them along a human chain until they reach their destination. The Hungarian border guards, equipped with obsolete computers and dilapidated vehicles, are being swamped by this human tidal wave
General Dezso Kovacs of the Gyor border guards said: "These are hi-tech networks, stretching from the departure country to the organisers in Budapest and the contacts on the green border.
"The migrants are either provided with forged documents or smuggled through."
Hungary is now coming under diplomatic pressure to tighten its borders. With Poland and the Czech Republic, also popular transit destinations because they border Germany, Hungary is likely to join the EU early in the next century. General Kovacs continued: "If the west wants Hungary to be an EU border country, it should give us more help. We have no computers at all on our eastern border."
Istvan Dobo, of the Budapest Office for Refugees and Migration, said: "When Hungary joins the EU it will have borders with non-member states, somore people will head for Hungary and, because of Schengen, once they are here they will be able to travel freely in the EU.