The dilemma faced by the Indian government in Kashmir is particularly difficult.
Four foreign tourists are being held at an unknown location by Al-Faran, a little known extremist group which has already shown that it is prepared to kill.
Broadly the four options the Indians have are to give in to the kidnappers' demands and release 15 Kashmiri separatist prisoners, establish a rapport with them and negotiate a deal, appeal to the terrorists' better nature, or find them and mount a rescue operation.
The gap between the two sides has narrowed since the hostages were seized in early July.
The terrorists have reduced the number of prisoners they want released from 21 to 15, while the Indians have said that they would consider releasing five of them.
But the Indian government is reluctant to bow to all the terrorists demands because this would encourage further hostage-taking.
Even though this incident has dealt a heavy blow to the Kashmiri tourist industry, there are plenty of visitors elsewhere in the sub-continent who could be seized.
In Britain, it has become standard practice for police dealing with hostage- taking incidents to try to build a rapport with kidnappers. Telephone links are established, relationships built up by trained officers and psychologists brought in to help to plan tactics.
None of this is of any use in dealing with a group like Al-Faran, as contacts are either through intermediaries or through brief telephone conversations. If the terrorists were surrounded in a building or a hijacked aircraft it would be different.
Appealing to Al-Faran's better nature has already been tried, with diplomats and moderate separatists pleading for the hostages' release and advertisements being placed in newspapers.
The terrorists' reply was to behead Hans Ostro, the Norwegian hostage, and threaten to execute the other four.
Paul Wilkinson, Professor of International Relations at St Andrews' University, says that such appeals very rarely succeed. He believes the only option for the Indian government is to mount a rescue attempt, but admits that this would be a high-risk operation.
He said: "Such an operation might not be successful. The problem with a group like this is that they may be suicidal fanatics and they have also probably dug themselves into an area where it would be hard to winkle them out."
Professor Wilkinson said that terrorist hostage-taking has increased by 30 per cent since 1992, with tourists increasingly regarded as easy and high-profile prey.
He continued: "Very few countries can put their hands up and say they have been consistent about how to deal with this."
Even countries, such as Israel, which normally take a hard line on terrorism have given in to demands on occasions. The Israelis released hundreds of prisoners when a passenger jet was hijacked and taken to Beirut in 1985.
In the past, India has taken a tough line on Kashmir, often using brutal tactics which have boosted support for separatists in the mainly Muslim state. The present hostage crisis will test that policy to the limit.Reuse content