They also said the shape of a Nato-Russia deal, and of the mechanisms for consultation between Nato and other East European states, is emerging fast.
The structure is expected to be three-legged: an Atlantic partnership for co-operation with the remaining non-Nato states in Eastern Europe after the first wave of enlargement; a Nato-Russia council; and, in an unexpected development, a forum for negotiations between Nato and Ukraine.
Of the likely new members, Poland, with 40 million people, is expected to be the fifth most important member of Nato after the United States, Germany, Britain and France.
All new members will have senior officers in key Nato appointments. But Poland's size and military tradition will make it a key player. Slovenia is still a possible new member the first time round. Sources said the real problems were over Nato states ratifying a possible fifth member, Romania.
The invitations to join will be issued at the Madrid Nato summit in July, and Nato hopes the first new members may be able to join in time for the Alliance's 50th anniversary summit in April 1999, though this is said to be "not a target or a deadline".
Officials rejected suggestions that a final decision would be made at this month's Helsinki summit between Presidents Clinton and Yeltsin. There will be a North Atlantic Cooperation Council meeting in Portugal at the end of May.
The mechanics of enlargement are not the main problem, Nato now believes. "Russia handling" is one, and disputes between the Alliance are the other. "We are offering you [Russia] a very genuine and serious strategic partnership. Please make the most of it", one top Nato official said. "If they miss out on the next two years they miss out on a new culture".
He added that Russian misgivings about Nato enlargement had been acknowledged.
"They see us [Nato] as a mirror-image of the Warsaw Pact. They think we're going to put in Poland the same infrastructure they put in East Germany".
However, Nato is adamant Russia will not be given a veto over decision- making and Nato will not promise Russia that certain countries will never be allowed to join. Nor will there be any pledge not to conduct Nato exercises in Eastern Europe, or to deploy Western troops in new member states.
Ukraine, a state of more than 50 million people, which gave up the nuclear weapons it inherited from the Soviet Union is "a very big subject", and Nato plans to treat it as a mini-version of Russia, with its own forum for liaison with Nato. "We are going through all the same issues in front of the Ukrainians as we are with the Russians", a Foreign Office official said.
The Alliance's biggest problem is internal. The French want a European to take charge of Nato's Southern European Command (Afsouth), based in Naples, but the US and some other Nato countries have been adamant this should not happen because of the strategic importance of the Mediterranean.
However, there have been extensive changes in Afsouth since Nato moved into Bosnia in 1995. Instead of being a "US fiefdom with the odd Italian ", Nato officials said European Nato nations had moved into key positions in the command, particularly the British and Norwegians.
Nato planners have produced the first two plans based on scenarios for operations to be carried out by the Western European Union - the European group within Nato.
"It's the first step towards Nato doing the WEU's operational planning for it", a Nato source said.
It is envisaged that the Deputy Supreme Allied Commander Europe , usually a Briton and currently General Sir Jeremy Mackenzie, will take charge of WEU operations, using Nato troops.