Since the beginning of the modern Olympics in 1896, what are the only two countries to have participated in every game?

britain and greece

This may be a case of the Internet perpetuating incorrect information, but a humungous number of sites indicate that the two are Greece and Australia.

A humungous number of sites are correct. Many countries missed the 1980 and 1984 Games because of political boycotts. Here, we didn't allow such considerations to stand in our way. We were determined to show off our sporting prowess - such as it was.

I am the proud owner of a brand new and expensive book called "Athens to Athens: The Official History of the Olympic Games and the IOC, 1894 - 2004" by David Miller. (I actually won it on a radio competition.) At over 500 pages it has just about everything you could ever need to know. Great Britain has definitely participated in every games since 1896. Indeed GB have won medals at every games, which is more than can be said for Shady's "determined to show off our sporting prowess" lot. The medal table for the 3rd games of 1904 in St Louis does not include Australia!

The book I refer to is THE OFFICIAL IOC publication for the history of the modern games. (I'd trust this to be correct rather than any website.) I'm not disputing (for the moment) that Australia has participated in every games, but given that GB has, then either Greece has not, or, THREE countries have participated in every games! Additionally, "Chronicle of the 20th Century" confirms the medals table. (OZ - nil point). Re 1980, I watched the GB team competing in Moscow. If you check you will find a certain Duncan Goodhew won gold in the 100m breaststroke beating Russian Arsen Miskarov. Australian Peter Evans came 3rd.

In 1980 some countries didn't compete under their own flag. The British team for example represented only the British Olympic Association and paraded under the Olympic flag. That might be the trick to the answer DB.

Quite a few books and websites state that 5 countries have participated at every Olympics: Australia, France, Great Britain, Greece and Switzerland.

Australia did not exist as a nation prior to 1st January 1901, yet we all consider them as a participant at every Olympics - our Aussie flag wasn't flying at the 1896 and 1900 Olympics - there were 5 colonies on the island of Australia, plus Tasmania as the 6th.

Five countries have been represented at all Summer Olympic Games – Greece, Great Britain, France, Switzerland, and Australia, though not always as part of official teams. Out of these five nations only Greece has participated under its own flag in all modern summer Olympic Games. Switzerland is on this list even though they boycotted the 1956 Olympics in Melbourne - they had competed in the equestrian events several months earlier in Stockholm. France did not send a team to the 1904 Games but a lone Frenchman did compete for the USA and a mixed team. Also in 1896 Great Britain competed as part of the 'United Kingdom of Great Britain and Ireland', while Australia participated in 1908 and 1912 as part of a combined Australasia team with New Zealand.

https://www.topendsports.com/events/summer/countries/index.htm

I'm not sure about your statement "The British team for example represented only the British Olympic Association."

Whilst they may not have represented the tyrannical Thatcher due to her attempts to stop them going without actually passing legislation, the BOA (British Olympic Association) rejected her letters on 4 separate occasions AND they opposed 3 similar attempts at persuasion by Foreign Minister Lord Carrington. They certainly repersented their country and their countrymen.

They represented ME for a start.

There were plenty of Union Jacks to be seen as well, some draped around victorious Coe and Ovett in the famous 800m & 1500m battle of minds and bodies. In all that is written about the 1980 games, GB as a country took part and all the medals won by Coe, Ovett, Goodhew and others are shown as GB in the tables. They are also included under GB in the overall tables for the sum of all medals won by each country since 1896.

Whilst Thatcher might not have been there, EVERYONE ELSE WAS.

The question would be more accurately worded as, "Which 3 geographical regions have been represented at every Modern Olympics Games?" Only Greece has been represented as a single unity in a technical sense. Great Britain competed as the "United Kingdom of Great Britain and Ireland" in 1896. Great Britain technically refers to the geographical island of Great Britain but Team GB encompasses the four nations of England, Scotland, Northern Ireland and Wales, plus the three Crown dependencies in the Isle of Man, Jersey and Guernsey, and all the British overseas territories, except the Cayman Islands, British Virgin Islands and Bermuda, which compete individually. That is a lot of "countries" per se. https://en.wikipedia.org/wiki/Great_Britain_at_the_Olympics

In 1908 and 1912 Australia competed as part of a combined team with New Zealand. This was introducing New Zealand to their first Olympics, and they supplied 3 athletes to each of the squads. So theoretically Australia was the representing nation but combined with New Zealand and acknowledged their representation in the change of name to "Australasia." The country "Australia" has participated at every modern Olympic Games.