Few could have imagined when air strikes began in Libya in March that Colonel Muammar Gaddafi would still be in power two months later. But a stalemate has emerged. Nato air power has prevented rebel forces from being defeated but it has not secured victory for them. So the war is being escalated. Tripoli has suffered the biggest air attack so far. The French have announced that they will now send in attack helicopters. Britain is considering doing the same.

Washington has said that "time is working against Gaddafi" but political rhetoric seems to have outstripped what the military, constrained by the United Nations' March resolution, can deliver. The tacit strategy now seems to be one of "accidental assassination" – with the hope that repeated air attacks on Libyan command centres will do what cannot be admitted to under international law, and kill Gaddafi.

This is a perilous tactic. One strike has apparently killed Saif al-Arab Gaddafi, one of the Libyan leader's sons. Unlike his brothers, he was not a military commander or propagandist. The fear is that his father could use the death to harden diplomatic reluctance over the war, in Russia and China and among more wary allies, like Germany and Turkey, and incense wider Arab opinion. Even were Gaddafi himself killed, his son Saif al-Islam could take over and continue the war. A de facto partition of Libya looks possible. So does a collapse into Somalia-like factional chaos.

The horror of the current situation should not be underestimated. There are worrying reports of organised rape, with 295 instances now documented. But the lack of clarity about this operation, confused from the outset, is ever more apparent. Barack Obama and David Cameron have vowed jointly to continue the military strikes until UN resolution 1973 has been "completely complied with".

Yet what does that mean? With a cagey US administration eager to hold this "European war" at arm's length, that could eventually leave Britain and France bearing the military burden alone, with no exit strategy and no real idea of what might a post-Gaddafi Libya look like. These are dangerous times.