The touchy relations between the British and American allies during World War II are a principal subject of Robert Sherwood's landmark Roosevelt and Hopkins (1948) and Arthur Bryant's two stellar volumes based on the diaries of British Army chief Alan Brooke, The Turn of the Tide (1957) and Triumph in the West (1959); they were certainly not unknown to General Dwight Eisenbowex. So one does wonder at John Eisenhower's professed discovery of the difficulties of ""agreeing on a common strategy"" and his ""second, related conclusion"" that the two partners retained their independence. The rub is not just, however, that in recounting the course of the war in terms of the alliance he has nothing new to impart--but that, in key episodes (successive Churchill-FDR meetings, intermediate Hopkins missions), he virtually paraphrases Sherwood, in particular, and yet manages to give a misleading impression: crucially, of the first post-Pearl Harbor confab, ARCADIA, as an outright struggle for dominance decisively won by the US. Not only do historians date the tipping of power much later (after American forces built up, and, with American material strength, overwhelmed even the redoubtable Churchill), but the ARCADIA decisions had an inner logic concealed here. (Basing the Joint Chiefs in Washington reflected its geographic position between two wars, for one thing, as well as American material potential.) So from the outset the reader is seeing developments slightly wrong--and not seeing the unfoldhag historical and personal drama. This is not a book, moreover, for persons who already know WW II history. Eisenhower is to be admired in some respects for explaining everything (""In a day before all nations were equal,"" he writes, the lesser Allies signed a major document out of the limelight), but much is basic information; and--an overall difficulty--his decision to describe not only the ongoing relationship but also the joint military actions, up to D-Day, results in compressed accounts of much-chronicled campaigns. One has at once an unsophisticated rendering of the already-notorious (the personality of Montgomery, for instance); much obscure, though sometimes intriguing detail--pertinent (BBC broadcasts interpreted as slurs on American forces) and less so (the discomforts of high-level wartime flights); and, extracted from the memoirs of the principals (Churchill, Eisenhower, Montgomery, etc., as well as the aforecited sources), word of what comes to seem their every interaction--never mind the crucial where-and-when issues. The Eisenhower family connection is, in the outcome, an advantage: the General, we hear, had started to write a book on his relations with Churchill and Marshall, from which some material is drawn; and his very prominence (or over-prominence) gives the book some focus. Also, John Eisenhower has a manifest grasp of American military interrelationships. But a combination of a good, brief WW II history (like James Stokesbury's) and salient volumes on the workings of the alliance--to which must be added David Fraser's recent biography of Alan Brooke (p. 250)--would serve almost any reader much better.