IT is a crime too heinous to comprehend - a mother drowning her crying baby, a father strangling his little ones. Infanticide is perhaps the one transgression we refuse to accept.

For most parents, the overwhelming instinct is to protect their children, whether it is a lioness risking her own life to safeguard her defenceless cubs from a marauding male, or a mother scooping up her child from in front of a passing car. It is almost a reflex action, an unquestioned response which is part of every parent's make-up from the moment their child is born.

But, for some parents, that instinct is over-ridden by such a savage and violent impulse, when they are driven to take their child's life, that it leaves us utterly bewildered.

"The instinct to protect your children is so strong that there is no way you could say that a person who is going to kill their family is mentally OK," says Teesside University psychology lecturer Barry Sudworth. "When you are in a mental state of imbalance, you are not thinking in a logical way and this form of functioning makes us do things that, when we stand back and look at them, we think how terrible they are.

"But when you are in this state, you can't think like that and the normal constraints on behaviour are thrown out of the window."

The grim scene which confronted police officers and ambulance crews yesterday was all the more horrific, knowing the perpetrator was the father, and the feeling that it is an offence against nature ensures this sort of tragedy lives long in the memory.

Earlier this year, Leonard Hurst was jailed at Nottingham Crown Court for killing his two-year-old daughter, after his ex-partner told him their relationship was over. The 33-year-old fed a hose-pipe connected to the exhaust through the window of his car, although his intention of killing himself as well as his daughter failed when the car ran out of petrol.

In March, Phillip Austin was given three life sentences at Northampton Crown Court after admitting murdering his wife, eight-year-old son and seven-year-old daughter last year. The forklift truck driver said his wife had been nagging him and pressure from mounting debts had driven him over the edge.

After killing his wife in a rage, he collected his children from school, drugged them and then strangled them. Both children showed signs of putting up a struggle. Austin was found in a car in a layby on a country road, with his wrists cut.

Trial judge the Honourable Mr Justice Potts expressed the horror many people feel when he passed sentence. "I can't find words to describe this case," he said. "It is beyond the bounds of belief that a father can kill his wife and children within a few hours of each other."

And last year, brothers Christopher and Oliver Fairless were found dead in their beds, while their father's body was found hanging in the garage. The two boys, aged nine and six, had been staying with their father at his home in Lincolnshire, for the first time since their parents had split.

According to Dr Sudworth, the explosion of rage which can cause the death of loved ones is often the result of a gradual build-up of pressure. "Some of the pressures could be over professional expectations, the belief that they should be a successful person and maybe this was not occurring, or at least not in the way that might have been envisaged by the other partner.

"If someone feels they are not fulfilling their familial expectations, which could include the amount of attention they pay to the children or the way they deal with them, this sort of tension builds up inside them, often with no one else actually knowing it is there, until all of a sudden it explodes.

"Someone can be telling their wife that everything is all right, and it will have been a gradual build-up. They might have been feeling that they were not a good father for quite a while, and there might have been so sign whatsoever."

For some child victims, their fate may have been sealed when they witnessed the explosion of rage which saw one of their parents kill the other.

"If the children saw what happened, the devastation caused to them could have been too much for the father to bear," says Dr Sudworth. "Maybe they were in that environment where he exploded and killed his wife, and he was still in that state of imbalance and that continued. It is only later that he realises what he has done."

And, he says, on some occasions, along with pressures from a partner, financial worries or problems at work, the children themselves could be part of the problem.

"Children themselves are very demanding, without thinking they are demanding, and when they are causing so much stress that you feel you can't cope, they become another part of that pressure. They might be little pieces of the jigsaw and, even though problems with a partner are likely to be a bigger piece, they are still part of it.

"If you feel you are not performing as your family expects you to perform, and you are also faced with people complaining or pressurising, it is going to make you feel even more unfulfilled and no good."

But, however baffling the desperation which drives some parents to kill their own children might appear, it does not mean that their love for their offspring has disappeared. Instead, that most terrible of crimes may be an expression of the strength of feeling.

"If someone needs to get rid of their inner turmoil and sense of unfulfillment, it may be that they get rid of it on to their family," says Dr Sudworth. "That suggests how important the family is to that person's sense of themselves as a person. Perhaps they were a reminder of what had gone wrong in their lives and how they felt they were letting their loved ones down and letting themselves down."