Most lenders have some policies around foreign incomes so if you're in a strong financial position you can have a lot of choices. There can be some limitations however.
Verification of income can be tricky for some countries. In Australia you usually don't need more than a payslip or two. Depending on the country and currency you're being paid in, you may need additional documentation such as employment letters, bank statements verifying deposits, employment contracts and tax returns.
The best advice I've got here is to have your income deposited into a bank account which issues genuine looking statements.
The bigger the deposit the better. Again it can depend on the currency of the income, but you can usually rely on being able to borrow 80% of the property value or contrat price. A few lenders will only allow you to borrow 60% to 70%. ANZ and CBA will lend up to 90% or even 95%, but there are limitations (especially for 95%; I don't think I'd even bother trying in most cases). Whilst these two lenders may be more generous for LVR, they have limitations in other areas.
Affordability may be determined differently. Some lenders have different policies for determining how much you can borrow. They can treat income and debt differently to Australian residents. This will potentially effect how much you can borrow.
Things take a bit more time. Don't agree to 30 day or 45 day settlements. Many things can be done over the phone or by email, but some things have to be done via regular mail and this takes time. You can also expect to be required to visit a consulate to get various documents certified, which can be a serious time waster. Transfering money for deposits can be tricky. Minimum timeframes to settlement should be 60 days, 90 days is preferred and 120 days is ideal.
Even if you're in Australia but have an overseas income source, many of the items above may still apply. Foreign income is certainly not the end of the world, but it does create some additional challenges which you need to be aware of.