PATRICK ANDERSON has written a first-rate book, a superb roman a clef about Washington, the White House, the men and women around a mildly philandering president -- all in a capital city teeming with ambition, devious maneuvering and a cynical press.

Unfortunately, First Family is not that book. Anderson's last novel, The President's Mistress , was the book I've described. It had everything, including a more-than-passable mystery, some memorable characters and a description of how things really happen in his fictitious Washington that was as good as anything I've read, fact or fiction. The President's Mistress , as a "Washington book," made the works of Allen Drury, for instance, seem as sophisticated (and as literary) as Rebecca of Sunnybrook Farm .

But First Family is -- as the sportscasters say -- something else. With all the talk, and all the rumors (a really classy one had Anderson's wife, Ann, fired from Mrs. Carter's staff because of the book -- untrue, as it turns out), those of us who fancy good trash novels were anticipating something pretty high on the scale; we rate Patrick Anderson as the Dick Francis of policitics.

Alas, even the clef lets us down. There is, to be sure, a Southern-ish (Tennessee) president who parlayed one term in th Senate and an anti-Washington campaign into the White House, and his intelligent, levelheaded but vulnerable wife. There is a broad array of characters from whom readers may select their favorite lookalikes: the smart, if brutal and insensitive, young aide; the idealistic, but weak and time-serving, domestic issues adviser; assorted ladies with loose morals and hearts of good; a few good-old-boy advisors with lurid political and financial pasts, and a collection of reporters, columnists and bureau chiefs. (One columnist with a Slavic name, "the most university disliked... in Washington..., a dour, dark-visaged little man who was often called the Black Prince or the Prince or Darkness..." is further described by Anderson as a man who hates liberals and never molests his sources. He is, of course, wholly fictitious).

But this cast is almost always around in Washington. Anderson's President Painter is frugal, dislikes presidential pomp, and is apparently humorless. Readers are, of course, supposed to think of Jimmy Carter; I found myself conjuring up an image of Calvin Coolidge. Anderson's young aide, a kind of Jordan-Powell-Moore mix, complaining to his president about the Congress and its unresponsiveness, could have just as easily been the Coolidge assistant who complained to his boss that "there are a lot of SOB's in the House, and we ought to do something about it." To that, the memorable presidential reply was, "There are a lot of them in the country, and they're entitled to representation."

Anderson has been in this city since the early days of the Kennedy administration (when he served in the Justice Department). His career has combined writing and politics, and in the 1976 campaign he was he lead speech-writer for candidate Jimmy Carter. He knows campaigns; he knows the Washington press; and he knows the infighting that often characterizes administration. And his ear for Washington speech is awfully good. Halfway through the book, he devotes several pages to a conversation between a reporter-turned-staffer and a veteran correspondent that is worth the price of admission all by itself.

When his ex-reporter explains that he quit the news business because he got tired of interviewing -- every year on the anniversary of her accident -- a woman who still loved her husband, even though he had hired someone to try to kill her, leaving her maimed and scarred,there is hardly a reporter who will not empathize strongly. And when he is then asked, "Why are you people running this country?" and he answers, "All I can tell you is, the son of a bitch was there for the taking," the reader is stunned to recongnize that in more than one administration that may be the best answer of all.

The plot of First Family , however, leaves one wondering, not about Patrick Anderson's Washington experience or his insight into Carter-ish behavior, but whether or not he was too influenced by those early 20th century novels about Christ figures who mysteriously appear, set things straight and then go on their way.

The psychiatrist in First Family restores marriages (including the First) from the shards of misunderstanding and neglect, provides insights into the behavior of villains and the moral strength with which to fight them -- so that all these White House staff folks come out fighting, decent and reunited with their spouses. He seemed to me more like the mysterious roomer of Jerome K. Jerome's play The Passing of the Third Floor Back than any political psychiatrist of fact or fiction.

In this city, nothing comes out neat.