AS Americans watch the challenges to the unity of states in Russia and the former Yugoslavia, the possible break-up of a major state looms on their own frontier. On Oct. 30, the voters of the province of Quebec will consider again whether to separate from Canada. The ballot will ask voters whether they agree that ''Quebec should become sovereign, after having made a formal offer to Canada for a new Economic and Political Partnership.'' Under the legislation authorizing the referendum, if the ''yes'' vote prevails, but such a partnership cannot be negotiated by Oct. 30, 1996, Quebec would declare independence anyway.
The people of Quebec have long claimed that they represent ''a distinct society'' within Canada. Visitors to the province, and especially to its rural areas, understand the claim. French predominates; many signs are only in that language. A continental European atmosphere exists different from that in the rest of the country. For those south of the Canadian border, it is as if a major portion of the Louisiana Purchase kept the language of Napoleon, was predominantly Catholic, and felt discriminated against by the country's English speakers.
The politics of the referendum are complex. The prime minister of Canada, Jean Chretien, himself from Quebec, leads the ''No'' forces. The three parties in Quebec that favor separation negotiated for several months to overcome differences on what form it should take. Polls consistently showed that, while Quebec voters believed their status should improve, the majority did not wish to separate. The legislation, therefore, promised economic links and the continuation of pensions and the use of the Canadian dollar. These promises apparently help the independence cause; one poll showed 50.2 percent would vote ''Yes.''
Polls show that the greatest fear of many Quebeckers is that independence will mean economic loss. As the campaign heats up, the ''No'' side will stress that, whatever the question says about ''partnership,'' no guarantee of such partnership exists in Ottawa. In fact, most observers believe that the western provinces, in particular, would strongly oppose any special dispensations to an independent Quebec.
The move to sovereignty has brought further complications. Even some of those espousing a ''No'' vote continue to look for constitutional compromises that might forestall separation. And the Inuit native population, in Northern Quebec, will have their own vote in Nunavik Oct. 26 on whether Quebec should be sovereign. They will also vote in the general Oct. 30 referendum.
The United States clearly cannot remain indifferent to the future of Canada. US administrations have tried to remain apart from this internal Canadian problem, although, on occasion, US presidents have given subtle support to one Canada. The prospect that Canada might split has implications for the US. Quebec represents one-quarter of the Canadian population. Strong economic links to the US exist; Quebec supplies substantial power to New York State. Defense relationships with the northern neighbor, including facilities in Quebec, are part of Washington's basic national-security strategy. Links are strong between the northeastern states of Maine, Vermont, and New Hampshire and the Maritime Provinces of Canada.
Throughout the world national structures are challenged by those who believe they are not receiving fair treatment from central governments dominated by other ethnic or language groups. If separation would resolve internal problems and create a better and more secure life for people on both sides, few would argue against such separation. In Canada, a ''yes'' vote Oct. 30 will test whether, in the long run, a break is the answer. Clearly, many in Quebec, itself, have their doubts.