The Council of Ministers is the balancing judicial/executive body to the King of Zanorre.  With the exception of the Minister of the People, the nobility vote on the election of Ministers to the Council.  Once having won the popular vote of the nobility, the Minister Hopeful must be approved by the King.  He (or She...) will then be a Minister, with all the powers and privileges that come with it (higher salary than that of most of the noble family; ability to influence laws; various powers of each Ministerial seat).
In law-making, only a Minister may propose a law.  Once proposed, the Council debates it and votes on it.  Changes may be made before the voting takes place.  Once approved by the Council, the King must approve it.  If he approves it, naturally it is law.  If he does not, the law may be re-written or changed to try to find his approval again.  Once changed, it will need to be re-voted on by the Council.  If approved a second time, it will go before the King again.  He must approve the proposal now or it will not be a law this time around.  Naturally, one could always start over again, but the same proposal is generally put to rest for at least 6 months.  It's not law, just tradition.
Occasionally the King and the Council will sit in judgement on a member of a noble house who has so egregiously broken the law as to need correction above the norm.  The King is the Head Justice, and the Council are Supporting Justices.  They must come to a majority decision, with a minimum of 6 (so that one Justice will not sway the entire vote) in passing judgement/sentence/etc.  This special court rarely takes place; most nobles either get off entirely or with a light warning.  If their crime is something that cannot be ignored, they are usually tried by the regular court system.  Examples of crimes for which the special High Court would be convened include treason, attempted murder of the King or a Minister, attempted murder of the royal family, or supreme insubordination.  It is decided on a case by case basis whether or not the crime is severe enough to convene the High Court.

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Chief Minister, Minister of Zanorre - Domestic Affairs Minister, and Head of the Council.  Position currently held by Lord Zuun, of the royal family.  Traditionally the Chief Minister is always of the royal family.  
Lord Zuun is considered a fair, even man, with some conservative leanings.  He is nothing if not patriotic, and very loyal to Riktal, to the point of ignoring other members of the royal family (especially Ilexia, whom he patronizes and still insists on treating like a child).  Has a few spies, mostly scattered around the noble houses and the palace.
In the question of who the princess should marry, he favors Herig, but as long as she marries either of the twins, he will not quibble.

Minister of Finance - In charge of the Royal Treasury and the Mint.  Position currently held by Lord Baen of the noble Kerlon House (kerlon = horse), the noblest house outside the royal family.  Kerlon House is always represented in the Council in some way.  Baen, as a younger man, worked at the Mint; he is the only Minister of Finance Zanorre has ever had that actually knows how the machines there work.  Has no spies, but personally knows most of the people working at both the Treasury and the Mint, and can call in favors.  He is deeply conservative, and believes the princess should be wed to Quin, who is technically the oldest of the twins (by a matter of minutes, but still oldest).

Minister of Foreign Affairs - Diplomacy and War; this Minister is the only one who can propose declaring war on another country.  The other Ministers must, of course, approve.  Currently the Minister of Foreign Affairs is Lady Vyncka of the noble Yeon House (yeon = swan).  She is the only woman to have held this post, but will probably not be the last.  She is a kind woman, with liberal ideas towards home, but rigidly strict rules towards other nations.  Her spies are more foreign than domestic, but she does have them just the same.
Believes that Ilexia should marry Quin, and SOON.

Minister of Security - Insures safety of the King and his family, as well as all of the noble houses, and all of Zanorre.  Law Enforcement, Courts, etc.  Lord Tay of the noble Kint House (kint = oak tree) is Minister of Security at the moment.  He has spies EVERYWHERE.  It's his job, after all.  Believes everyone is free to do as they wish, but must pay the consequences of their actions - more of a hard-line justice sort of person.  Thinks the law is already too lenient.
He believes Herig to be the better choice for the princess; Herig's magical capability would be most useful in matters of security.  

Minister of Industry - Magic and Science, including creation of Mechanica.  Lord Genart of the noble Genova House (genova = storm) holds the post at current, and is every inch the businessman turned politician.  The bottomline is always his utmost concern.  Rigidly conservative; spies are few, but very good.  Naturally, overseeing the creation of Mechanica, he is well in favor of the princess marrying one of the twins, preferably Herig, since he's the main magic-user of the two.

Minister of Agriculture - Oversees crops and farms, to make sure the Zanorran people have enough food and drink.  This Minister is currently Lord Humvelt of the noble Beron House (beron = mountain), the second son of a second son.  Berons do not usually get too involved in politics unless it concerns them, but Humvelt actually cared enough about other people to try for and win the Ministry position.  While never having actually grown anything himself, he's a gourmet chef and has an extensive vegetable garden for his own use on his estates.  He knows good food from bad, and the basics behind what makes them which.  He has spies (he got them after he discovered everyone else had them), but they are seldom used.  He favors Ilexia marrying Quin so that the whole thing will be over and done with and they can get back to more important matters.

Minister of the People - Minister appointed by popular vote of the Zanorran people.  This position was added a scant 100 years ago when near-revolt rocked the country and the Council deadlocked on what to do.  This way, not only are the people's voices heard, but the Council is expanded to 7 Ministers, meaning there can Never be a tied vote (as abstaining is not allowed).  Position currently held by Master Rugard, a former blacksmith.  Very well educated, he won popular vote after the last Minister of the People was found to be accepting bribes.  He is an honest man and speaks his mind (perhaps a bit too often - tact is not one of his strong points).  Very much a man of the people.  He does like to get drunk, but only does so on special occasions (unfortunately, these tend to include state dinners and formal balls), and never imbibes before or during Council sessions.  Very affable, with a fair distrust for politicians but a hearty love for "this great nation of ours."  Likes to give strong backslaps, and thinks Ilexia should marry whichever one of the twins she chooses (better than the other Ministers, but still not perfect).