In a development that could have national implications, the federal government has notified 36 property holders in northern Minnesota that they might not own their land.

The land, the notices suggest, may belong to Indians, descendants of tribes that were scattered at the turn of the century when the government broke up the state's reservations.

The challenges, affecting a total of 125,000 acres, are the first of hundreds expected to question ownership of properties now occupied by individuals, businesses, counties, and the state of Minnesota.

The action came after federal Bureau of Indian Affairs investigators here uncovered forfeitures and sales of Indian land that they now consider illegal. The Minnesota BIA agency's move has national implications because similar investigations are under way in other states.

The Minnesota investigation was triggered when Congress, seeking to tidy up Indian claim litigation, set a clsoing date for bringing such lawsuits on behalf of Indians. After April 1, Indians can sue on their own.

The Minnesota BIA, looking into what happened to Indian lands when the government broke up reservations, found that each tribal member had been awarded a parcel of property, in most cases held in trust by the government. The rest of the land was made available to private interests, homesteaders or for public use.

In the disputed cases, the tribal member's land was put on state and county tax rolls and, when taxes were not paid, was sold at forfeiture to non-Indians. Such sales, the BIA investigators say, apparently were illegal. Other cases stem from sales without consent of the owners and other irregularities.

Some examples:

Land was loaned to a mission. The missionaries left, but the land was never returned.

Land was preempted for a railroad that was never built. The company dissolved, but the land was not returned.

An entire township near the present-day town of Effie was set up for Indians. The Indians have moved away and the disposition of their land is in question. This "lost reservation" no longer shows on most maps.

The Minnesota investigators have been hindered by sketchy information and fragmented Indian heirship.

In one typical Standing Rock case, an Indian received 320 acres in the 1890s. Since then, this land has gone through 218 probate actions. There are 374 known heirs, of whom 58 have shares of one acre or more, and 316 have shares of less than an acre. Few of the 374 know where their land is located.

Rex Mayotte, superintendent of the Minnesota agency of the BIA, who appointed the research team, cautions the individuals involved in the current cases that which cases actually will be litigated is up to the Department of Justice.

In the absence of such action, there has been concern in the real estate community. Brokers have advised clients to obtain thorough title searchers when purchasing land once owned by Indians. Title insurance for northern Minnesota land is difficult to purchase.

Among tribal leaders, meanwhile, the investigation has produced approval tinged with outrage.

"We had complained about these things all our lives," said Leech Lake Chairman Hartley White. "When I came back from service in World War II, the people told me about BIA selling their land while we were gone. Nobody listened to us. Nobody would do anything. Now you tell us!"