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I know I'm likely to be told to find myself a steuerberater
Well, you did say it yourself!
However,
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-- obligations on the landlord
Obviously the main one is keeping the house in good order and if you haven't got a good agent, you'll find that most German tenants are pretty quick to cut their rent payments if there's a problem - and the courts are usually pretty much on the side of the tenants.
One oddity to be aware of; it's the reponsibility of the owner to see that the snow gets cleared promptly. Make sure this is unloaded onto the tenant in your rental contract.
Speaking of contracts, it is well worth using one of the ones prepared by Haus & Grund or similar organisations. Yes, you have to join them, but it doesn't cost much and there are other benefits as well.
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-- local tax, if any, on income from residential letting
Yes you'll need to tax any profits here. I don't know about Portugal, I would doubt it, but in any case, inside the EU I would expect that all to be covered by double taxation agreements.
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-- any possibility to claim loan repayments claimed against rental income
You can offset the interest, not the capital repayments, against rental income.
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-- any possibility to claim loan repayments claimed against rental income
I believe you can offset most maintenance and repair work against rental income. If it's genuine modernisation which improves the quality of life (new central heating, better TV system, etc.) then you can also increase the rental by a proportion of the investment costs. I'm not sure how much this is, but if you're on this route you'll need some advice anyway to be sure that your investment is genuinely improving the quality of life. Putting in a new central heating or better insulation which resulted in the tenant having to pay 30% less for his heating costs would be an improvement. Replacing Cable TV with Satellite might not be (unless the tenant had been paying the cable costs, of course!).
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-- any capital gains tax in the event of selling the property?
If you've owned the house for less than 10 years, then yes. However, you only pay tax on the profit and in the current state of affairs in the German housing market, unless you've owned the house for about 20 years, that's a pretty unlikely scenario!
In general, I would definitely advise getting an agent, however, probably because of the smaller market here, the agents don't seem to be as competent or reliable as in the UK. If you let us know where the house is, perhaps somebody local might know somebody.