NOTWITHSTANDING REPEATED mutual assurances that there is nothing for others to worry about, the fighting in Kashmir between India and Pakistan becomes steadily more dangerous. The action in the high Himalayas, already more serious than it has been for decades, is relentlessly sharpening the question of whether the two South Asian rivals, both now nuclear-capable, can maintain control.

This time around in often-contested Kashmir, the Pakistanis are plainly to blame for having started the fighting. If it was not the elected government of the country that was responsible, then -- perhaps worse -- it may have been a sort of Pakistani military-fundamentalist axis that the government is not in a position to know fully about, let alone to subordinate.

In an evident act of provocation, hundreds of Islamic guerrillas from Afghanistan and elsewhere and perhaps also some Pakistani soldiers infiltrated across the "line of control" -- the temporary or unofficial border -- separating India- and Pakistan-held Kashmir. The evident military purpose, beyond political challenge to the Indian government, was to put at risk the strategic Kargil highway by which India asserts its military presence in that mountain fastness.

To this Pakistan-inspired initiative, the Indians responded vigorously by sending warplanes with precision-guided weapons against guerrilla positions. The Indians have so far been careful, however -- this to the Clinton administration's praise -- not themselves to cross the line of control. In this high-altitude confrontation, the infiltrators have the higher ground, but powerful India would seem to have the military edge over time.

The danger the confrontation poses arises from the newly achieved nuclear status of the two South Asian countries. In particular, the reaction of Pakistan or its headstrong generals or its struggling civilian leadership to a prospective humiliation at the hands of India makes for a pervasive nervousness.

In the year after India kicked off nuclear tests by itself and Pakistan, the United States launched a diplomatic initiative intended to deepen the two neighbors understanding of the implications of joint nuclear status for peace and stability in their countries and in their region. With the now month-old Kargil crisis, the emphasis of American diplomacy necessarily has shifted to cooling down the military inflammation -- Washington calls on Pakistan to withdraw support for the guerrillas -- and drawing the combatants back into the so-called Lahore process of talks and a few tentative but resonant acts ("bus diplomacy") between the South Asian rivals. From President Clinton on down, the administration has been promoting the Lahore option in order to impart to it a momentum of its own and to help South Asia rise above the deep distrust otherwise drenching the subcontinent.

Divided Muslim Kashmir, already the cause at the center of two wars between India and Pakistan (when they were both much less lethally armed than they are today), remains the hard case. It is the single issue that most stirs strategic anxieties as well as nationalistic passions on both sides. In the past, other countries could, and generally did, regard that hot spot chiefly as disagreeable and dangerous but as a piece of business falling mostly between India and Pakistan. But with the two now having declared themselves nuclear powers, and showing themselves not in full respect for the cautionary rules of the nuclear road, then the circle of the concerned expands.

Fortunately, not all the signs in South Asia point the same way. American officials take heart that both sides are listening to their cautions. The officials hold out some hope for a diplomatic resolution of the Kargil crisis. But that's much the lesser part of it. If the Kargil crisis is calmed there must come a serious address to the Kashmir question.

Pakistan needs to stop blowing on the fires of armed revolt in India-held Kashmir; this is basic. But India has its own responsibilities. The Indians want it both ways: to keep a tight grip on Kashmir and at the same time to deny Pakistan's effort to "internationalize" the issue; the Indians would confine it to exchanges between India and Pakistan. India can sustain this rigid posture, if at all, only by systematically and credibly widening the openings for democratic self-government in the part of Kashmir that, with two-thirds of a million troops, it holds.