You know those bike-sharing programs that have sprouted up in many American cities?

They're the ones where you rent a bike from a terminal in one part of town, ride it to another neighborhood, and drop it off at a second terminal.

We have one here in Boston, called the Hubway. New York has one too, Citi Bike. Most of us have a company from Montreal, Canada, to thank for that.

The company's called Bixi — and it's successfully exported its model to several cities in the US and around the globe.

But the company that runs Bixi, Public Bike System Company, filed for bankruptcy protection recently. It says it owes creditors, including the city of Montreal, nearly $50 million.

Suzanne Lareau, president of Montreal nonprofit Velo Quebec, says that, financial troubles aside, people love Bixi.

"We like it. It’s part of Montreal," she says. "It’s very important for the Montreal, not only for the citizen, but also for everybody; the financial community. Bixi is a part of our personality.”

So how does something that is hugely popular, with millions of rides taken each season, wind up having financial problems?

Lareau says it’s complex, but she thinks it boils down to two main problems.

The first, is the city of Montreal wanted a return on research and development investment faster than the company could achieve. The second, is the city needed to invest in Bixi’s operational costs.

Montreal has bailed out the company that runs Bixi in the past. It 2011, the CBC reported the city approved a $108 million bailout for the company: $37 million to cover Bixi's deficit, and another $71 million in loan guarantees to export and develop the system abroad.”

Essentially, Bixi was one company with two different divisions. One operated a bike sharing system in Montreal. The other worked to export that system to cities around the globe. And that development is the one that many say hampered Bixi’s ability to stay profitable.

Forbes created a handy cheat sheet on the money Bixi owes and the money owed to Bixi:

New York and Chicago: They owe Bixi $5.3 million, withheld because of delays in implementing software across the Citi Bike and Divvy Bikes systems respectively.

Damages: Alta Bike Share, which operates Citi Bike for New York, wants $11 million from Bixi because of those software delays.

Loans: Bixi owes Montreal and its taxpayers a minimum of $38 million. About $31.6 million is owed on a $37 million loan from the city. Another $6.4 million is owed on a line of credit guaranteed by Montreal taxpayers.

Suppliers: They are owed $9 million by Bixi.

Montreal: Beyond the loan and line of credit, it could cost $1.5 million more for Montreal to run the Bixi system in 2014.

Lareau says the sorry state of Bixi is sad for the both bikers, and the citizens of Quebec. She says it was a good idea. And the system works great in Montreal. (As someone who rode the Bixi during a stay in Montreal, I must agree. It allowed me to leave my car parked during my entire stay.)

Montreal Mayor Dennis Coderre says Bixi will run in 2014. But there are no promises for the following year. And that concerns people in the bicycle community. People like Lareau.

“You know, we’re in the 21st century and Bixi is an important part of our commuting operation around town,” she says.

Officials at Bixi declined an interview request, but offereed this statement:

On January 20, the Public Bike System Company (PBSC) filed for protection under the bankruptcy and insolvency act. This means that as of today, our doors are still open for business and that as of today it is business as usual. In the coming days representatives from the City of Montréal and PBSC are going to sit down and talk about the scenarios currently on the table. So short term speaking, it's business as usual. Now as for long term, it’s a bridge we will cross once we will get there.

Hopefully, for lovers of Bixi, that crossing will happen by bike.