Buying a house in US on TN or J1 visa

I am a Canadian citizen working on TN visa and my wife is on J1 visa. We are thinking to buy a house here in US. My mortgage is approved and everything seems to be working. But, I am wondering is it legal to buy a house in US on TN or J1 status? I will transfer money from Canada to US for the house any issue?

There's nothing to stop Kim Jong Il buying a house in the US if he wanted to. Staying in the US and living in it is the trick.

Steve,
is buying a house in US not an intent to stay permanent which against TN rules?

Perhaps but as far as that goes it's more what you have on you when you arrive at the POE which is more relevant, they want evidence the stay is temporary. Plenty of Canadians have houses in the US and don't live there, and whether you rent or own, you still have an abode in the US. So yes it might be a factor but a relatively trivial one.