Kim Jong-nam had been living in exile in South-East Asia.
But while he was a critic of the President's leadership, the 45 year-old was not widely considered a serious threat to the North Korean government.
Authorities say two women attacked Kim Jong-nam with poisoned needles at Kuala Lumpur airport in Malaysia before he collapsed and died en route to hospital.
The suspected assailants fled in a taxi.
As the eldest son, Kim Jong-nam was once in line to inherit the presidency from his father, Kim Jong-il, the late North Korean ruler whose birthday is being celebrated tomorrow.
But he reportedly lost favour with his father over a fake-passport scandal in trying to visit Japan and Tokyo Disneyland in 2001.
The top job instead went to his younger half-brother, Kim Jong-un, and that is where suspicion now lies over his death.
But Britain's former ambassador to the country, John Everard, has told Sky News nothing can be certain when it comes to the secretive state of North Korea.
"If you have a nation whose royal family are starting to kill each other in foreign airports, it's not a good sign of political stability. But it may not have been Kim Jong-un. There are all kinds of factions within the North Korean regime. There are various people who might have wanted Kim Jong-nam dead. And it may be some time before we firmly establish who was behind this killing."
In exile, Kim Jong-nam has been a critic of his half-brother's government.
But his apparent assassination has also surprised another North Korean analyst, Aidan Foster-Carter, with Britain's Leeds University.
"I'm gobsmacked, as they say. I suppose that there are (reasons) why this might have happened, but I certainly wasn't expecting it now. Kim Jong-nam was in exile. He had been a bit of critic -- unwisely, indeed, as it turns out -- some years ago of his brother Kim Jong-un and, indeed, of the whole idea of hereditary succession. But we hadn't heard from him for some time, and I assumed he was lying low and that he wasn't really a threat to anybody. But it would seem perhaps his half-brother thought differently."
North Korean analyst Dr Leonid Petrov, at the Australian National University in Canberra, says there was no doubt the half-brothers were not on friendly terms.
"Partly because he comes from a different branch of the Kim dynasty, and also Kim Jong-nam's son was very vocal, giving interviews where he criticised the North Korean succession system. And even at some stage when he studied in France, Kim Jong-nam's son was threatened to be kidnapped and taken to North Korea. So there was a lot of bad blood between the two half-brothers, and potential assassination is conceivable."
But Dr Petrov also suggests other potential suspects.
"Because Kim Jong-nam was involved in some murky dealings in South-East Asia, raising money for the family, so, potentially, it could be organised crime, some mafia groups in South-East Asia, in Macau. He often travelled to China and Russia. So, potentially, there could be different scenarios and suspects."
Aidan Foster-Carter points out there is a history of Kim Jong-un taking steps to rid himself of family rivals, though.
"He did, of course, very famously -- and this is the precedent in everyone's mind -- he had his uncle, Jang Sung-taek, a one-time mentor who helped him succeed, he was executed, allegedly as a plotter and goodness knows what else, in 2013. I can see why he might have thought the uncle was a threat. Kim Jong-nam, I'm surprised at that. But as I say, maybe uneasy lays the head that wears the crown."
There is also speculation neighbouring countries uneasy with North Korea's military ambitions and its unpredictable leader were seeking to have Kim Jong-nam take that crown.
