After discovering the problem was electrical, the van was taken to a workshop and parts ordered, leaving the couple with no transport or anywhere to sleep.
"So they had no form of transport and they didn't know how long the van was going to be off the road so we asked if they would like to stay with us," said Mrs Groves.
Mr Oberfalcer said he and his wife had been travelling around the North Island for the past four months and working on organic farms and on orchards.
"We had a problem near Auckland with the spark plugs so this is our second problem with the van," said Mr Oberfalcer.
This time it turned out to be the fuel pump.
The vehicle had stopped about 300 metres from the Groves' home.
"It was a really bad feeling because we are in a country where we don't know anybody, we haven't got any friends here so [breaking down] was a bad feeling," said Mr Oberfalcer.
The pair had walked to the nearest house to seek help.
"It was Trevor and Mavis and they helped us - it was absolutely amazing. They called the garage and because our English is not good - it's really quite hard."
The purpose of the couple's visit to New Zealand had been to improve their English-speaking skills and see the country's natural beauty.
Mr Oberfalcer said he had been impressed by people's friendly nature.
"In Czech Republic every second person doesn't help because you're a stranger and they don't trust the people."
Mr and Mrs Oberfalcer had offered to earn their keep by gardening for the Groves, who declined the offer and instead insisted the couple made themselves at home.
The couple expect to hear from the mechanics today.
"If somebody from the garage says everything is okay, we will go to Martinborough and after we will go to Wellington. We will spend a few days and then ferry to the South Island."
The Oberfalcers plan to spend three months down South then return to the North Island, before heading back to Czech Republic in February.
