If I don't have the nationality of a country, how long can I stay in that country at most, provided that I am a non-immigrant country.

First of all, if you enter that country legally, you must first get an entry visa for that country.

Second, if the visa you get is not an immigrant visa, it must be a visa with a time limit, such as 10 multiple-entry visa. In most countries, 10 year is almost the longest among non-immigrant visas.

Third, even if you get a visa valid for 10 years, it does not mean that you can stay for 10 years after entering the country. When you enter the country, the immigration officer of that country will stamp an entry stamp on your passport, which will indicate how long you can stay in that country. Generally speaking, three months is a long time. After the expiration of three months, you must leave the country, then enter the country with a visa that is still valid, and then obtain a new legal residence period.

Fourthly, the situation in Monaco you mentioned is quite special. Although Monaco is not a Schengen agreement country, it recognizes the Schengen agreement, and citizens of all Schengen agreement countries can freely enter and leave Monaco. In addition, Monaco is a tax haven, so many wealthy Europeans have settled in Monaco. So what you said happened: half of Monaco residents have no Monegasque nationality. However, it is not easy for non-Schengen nationals (such as China people) to settle in Monaco. Monaco is a pocket country, bordering only France, so you must enter France first and then Monaco. Although there is no border inspection between Monaco and France, you have to go through legal entry formalities in France first. So this goes back to the above three questions: 1, you have to get a Schengen visa first; 2. How long is your Schengen visa valid? 3. When you enter a Schengen country (such as France), how long is the legal stay period given to you by the entry border inspection officials in that country?

In short, if you don't have the nationality of a country and the permanent residency (green card) of that country, it is impossible to legally live in that country for a long time.