Could an American visit the USSR for any reason or was it illegal?

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Time difference from Moscow https://bitly.com/31b7O8i

I have visited both Russia and Cuba in the past 5 years while on cruises.

In Russia, if you wanted to go about by yourself, you needed to apply for a visa. However, if you went as part of a tour arranged by the ship, you didn't need a visa, but you had to stay with the tour group at all times. Once the tour was over, you couldn't leave the ship.

On my cruise to Cuba (pre-Trump), I was able to leave the ship and go about on my own. 

It was not illegal or impossible to visit the USSR as a westerner.  However, western tourists were followed and watched by the security forces.

There are better answers, this is an FYI:

Even in the early days of post-USSR Russia, it was recommended to use "tourism" as my reason for travel to Russia, nothing else. The difficulty of entering the "Evil Empire" was for me more attraction. I made it in just in time to see Gorbachev toss it all away with his pen...EDIT: I was too rushed to remember to mention ALL visitors HAD to go thru Intourist on set tours. One could not "hop a train" to Kazan or Perm just to visit those cities. Intourist has special hotels for foreigners. Tours were $2500 or so and usually Moscow, Leningrad, and a few other cities.

YES but not for ANY reason.

Tens of thousands visited the USSR tourism was allowed. Covid 19 has its particular travel restrictions but travel is even allowed now.

You needed to obtain permission (a visa) from the officials of the USSR in most but not all situations you were part of a tour group.

USSR decided who could enter and you needed to have valid reasons to enter.

USA has similar rules for visitors FROM the USSR to the USA. A soviet citizen had an extra step in that they needed an "exit pass" to depart the USSR.

There has been DAILY flights from Moscow to the USA and the reverse for decades.

PANAM and Aeroflot had service back to 1968.

Before that you could get there but had to take an indirect route with a change of plane.

Waving your USA passport is not an entry pass to any country. Every country decides if the holder can enter their country.

One had to have the correct papers to get into the USSR but people visited.  Getting out was more difficult.

You do know that Lee Harvey Oswald traveled to the Soviet Union just before he turned 20 in October 1959.

It was rare that Americans visited the USSR, but it did happen occasionally, usually as part of some diplomatic mission. I remember when a group of scientists from Abbott Laboratories in my hometown was permitted to go there, the purpose of their visit being to assist the USSR in producing baby formula inexpensively in order to meet the nutritional needs of infants there as the orphanage crisis bloomed and orphanages were becoming overrun with infants being dropped off by mothers who couldn't care for them. Those that went were allowed to bring their spouses, and the spouse of one was my former 6th grade teacher, and she was so excited to go because she knew it was such an extremely rare opportunity, the only opportunity she'd ever had or ever would have to visit the USSR, not that that was anything she ever aspired to, but the fact that it was so extremely rare for an American to be granted permission to visit the USSR that it was like winning the lottery, like getting a one in a million chance opportunity.