Why and when should exchange rates change under a fixed - exchange - rate system?
Presumably, exchange rates pegged to each other will not change in relative terms. The whole point of a fixed exchange rate is precisely to allow one country's currency to always remain at a constant value relative to the other country's currency. Because the U.S. dollar has been the main reserve currency globally since the late 1940s, many countries have pegged their currency to the dollar in the hopes of being able to have a more stable economy, with preferential market access to the United States by virtue of its cheaper exports.
One of the most contentious issues between the United States and China over the last decade has been China's refusal to let its currency "float" freely against the dollar. During the mid-1990s, China fixed its currency to the dollar, but at a significantly weaker value than the dollar. By ensuring that its currency would always be weaker than the U.S. currency, China assured itself of a favorable trade balance. A weaker currency makes Chinese goods cheaper in the United States, and U.S. goods more expensive in China. Successive U.S. presidential administrations have raised the issue with the Chinese government, but to little effect, leading to charges from members of Congress that the U.S. is not being tough enough with China and is suffering economically as a result.
While China has taken steps over the past eight years to make its currency a truer representative of its actual value, it has done so only fittingly and minimally. The failure of the United States to break the fixed exchange rate between the dollar and the Chinese renminbi, or yuan, has meant that the trade imbalance continues to remain unacceptably high.
To answer the question, then, fixed exchange rates, by definition, do not change. When the imbalance between two countries' trade begins to disproportionatly favor the country with the weaker currency, and that currency is pegged to the currency of the other country, serious disputes are certain to result, with the country suffering in the trade relationship pushing the other to let its currency float, rather than be held at an artificially low value.