If I live nowhere, do I still have to file a tax return?
Almost always, yes. Having no tax residence at all is not a tax position, it is an unexamined one. Residence ends when ties end, and if nothing has displaced your old residence it persists, which means the country you left still expects the returns a resident files. Continuous travel does not create a gap in the system. It usually leaves the last clear residence in place while a second country begins to take an interest. So the filing question is answered by establishing the position first: which country has a claim, on what facts, and from what date. The returns follow from that, not from your itinerary.
Which country do I file in when I move every few months?
The one that still has a residence claim on you, which is usually the country you last lived in properly. Short stays rarely end one residence or begin another, so a year of three-month stops often leaves the old position untouched. A treaty tie-breaker cannot help here, because tie-breakers operate only between two countries that both claim you. If only one does, there is nothing to break. Start by listing the ties you kept in the country you left, such as a home, family, registrations, accounts and memberships, and the position becomes visible. The filing set then follows the position.
Can a treaty tie-breaker help me if only one country claims me?
No. A tie-breaker is a rule for resolving competing claims, so it needs two of them. Where one country treats you as resident and no other does, the tie-breaker never engages and the single claim simply stands. This is the part that catches people who travel continuously. They expect a treaty to relieve them, and the treaty has nothing to work on. The practical consequence is that relief often depends on establishing a genuine residence in some country, which gives the old claim something to yield to. Until then, the old country's rules decide what you file.
Do I keep filing as a resident after I sell my home and travel?
Selling a home is one tie ending, not residence ending. Residence ends when ties end, and the question is whether enough of them have gone, and when. People who sell up and travel frequently keep bank accounts, registrations, health coverage, dependants or a correspondence address, and any of those can keep the old position alive. The filing basis for a year is therefore a factual question answered before the return is prepared, not after. Build the list of ties as they stood through the year, fix the date each one ended, and the correct filing position for that year follows.
What documents show I stopped being resident in my old country?
The ones that record ties ending, with dates on them: the disposal or letting of a home, the closing of registrations, the ending of coverage, the move of dependants, and evidence of where you actually were. No single certificate settles it. Residence is decided on facts, so the file is a set of dated documents rather than one declaration. Keep them as the events happen. Reconstructing them years later is possible but slower and weaker. Where a second country is involved, its own evidence of your arrival matters just as much as the evidence of your departure.
Is having no tax residence a real position I can rely on?
No. It is the absence of a position rather than a position, and no tax authority recognises it on your say-so. In practice the last country you were clearly resident in keeps its claim until something displaces it, so the traveller who believes he is resident in no country at all is usually still resident where he started, and filing nothing. That combination is the worst of both systems: a live claim, no relief, and no returns. The better route is to decide where you are resident, evidence it, and file on that basis.
Do I have to declare my dual citizenship?
A tax return does not generally ask you to declare which passports you hold; it asks about residence, and in the US case it applies to citizens by definition. What does ask is your bank. Account-opening self-certification under FATCA and the Common Reporting Standard asks which countries you are a tax resident or citizen of, and the answer is reported onward to the tax authority. So the practical answer is that the information arrives either way. See FATCA reporting.
Does the Foreign Earned Income Exclusion apply to self-employment tax?
No — it does not reduce self-employment tax at all. The exclusion removes income from income tax only, so a US self-employed person abroad can exclude the profit for income-tax purposes and still owe self-employment tax on it. What can relieve that is a totalization agreement with the country where you actually work, which assigns you to one social-security system instead of both. See totalization agreements.