Your Royal Hostage, by Antonia Fraser. New York: Atheneum. 228 pp. $15.95. Jemima Shore, Megalith television's popular and attractive investigative news reporter, loses her job in a corporate shuffle and is promptly hired by an American television network to co-anchor the live coverage of the wedding of the Queen's cousin, Princess Amy of Cumberland.

Jemima aids the police in their investigation of the murder of a member of Innoright, an animal rights group that kidnaps the princess in order to promote its ideas about animal liberation.

Although the delightful Jemima plays a smaller role than usual, this is one of the best mysteries in the series. The plot is suspenseful, and Fraser's tone is slightly satiric in her depiction of the ruthless animal lovers, the royal family, royal weddings, and royal biographers. Fraser, author of several historical biographies, including ``Mary, Queen of Scots,'' has written five other full-length Jemima Shore mysteries and one collection of short stories. Hot Money, by Dick Francis. New York: G.P. Putnam's Sons. 324 pp. $17.95.

``Hot Money'' departs from the usual Francis formula by including elements of both a family saga and a traditional murder mystery, and the results are not entirely successful. Jockey Ian Pembroke is a typical Francis hero, a decent, quiet loner who is adept at standing up to bullies. There are quite a few bullies in ``Hot Money,'' all of them related to Ian. His father, Malcolm Pembroke, a wealthy gold trader, has been married five times and has eight children. Someone murdered the fifth wife, and now someone is trying to kill Malcolm.

Ian begins to suspect that the murderer is a member of the family, although most of them seem more like potential murder victims than murderers. Despite the chart provided by Francis, sorting out the members of this unpleasant extended family is a challenge.

Although the identity of the murderer comes as a surprise, the resolution is unconvincing and disappointing. It deprives the reader of the primitive sense of satisfaction usually found in a Francis scenario, in which a detestable villain, after beating the hero both mentally and physically, has the tables turned on him and is brought to justice by the hero. There is plenty of suspense, however - and some exciting horse racing scenes.

``Hot Money,'' though not his worst, is far from being Francis' best novel. Death for a Dietitian, by E.X. Giroux. New York: St. Martin's Press. 182 pp. $13.95.

Although E.X. Giroux lives in British Columbia, her mysteries featuring the sleuthing barrister Robert Forsythe and his secretary, Abigail (Sandy) Sanderson, are set in England. This is the fifth novel in the series, and like its predecessors, it is cozy, genteel, somewhat old-fashioned, a little silly, and very satisfying.

When Forsythe is unable to accept an invitation to play the detective at a mystery weekend on a private island, Sandy goes in his place. The game becomes real, however, when a famous chef is murdered, and Sandy, without Forsythe's help, must solve the crime.

The likable Sandy, a combination of Jane Marple and Jessica Fletcher, has now come into her own as a detective. The Black House, by Patricia Highsmith. New York: Penzler Books (distributed by Mysterious Press). 258 pp. $15.95.

In each of the 11 suspense stories in her latest collection, Highsmith, author of ``Strangers on a Train,'' creates an atmosphere of impending doom or potential horror that usually amounts to nothing much in the end.

In a typical story, ``Not One of Us,'' a group of friends subtly turns on an unpopular member of the group. He begins to drink heavily and, as a result, loses his job, his wife, and his life. His friends feel guilty; morally they are responsible for his death.

These stories, in which characters frequently take the path of least resistance, are almost banal in their depiction of the worst aspects of human nature. Highsmith charts the same psychological territory as Ruth Rendell but lacks Rendell's sympathetic touch. Who Saw Him Die? by Sheila Radley. New York: Charles Scribner's Sons. 202 pp. $14.95.

Radley's likable characters continue to grow and change in her sixth mystery set in the English town of Breckham Market.

Detective Chief Inspector Douglas Quantrill doesn't pay much attention to the accidental death of the town drunk, Clanger Bell, even though Bell's sister insists he was murdered by a new resident, Jack Goodrum. Quantrill is too preoccupied with personal matters: his attraction to his partner, Detective Sergeant Hilary Lloyd; his dissatisfaction with his marriage; his reluctance to accept his impending grandfatherhood; and his anxiety over his teen-age son's rebelliousness. Goodrum's murder, however, and his own son's serious injury in an accident force Quantrill to tackle both the murder cases and his personal problems.

Radley stresses characterization without sacrificing suspense.

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