The citizens of the United States who accompanied the late Texan expedition to Santa Fe, and who were wrongfully taken and held as prisoners of war in Mexico, have all been liberated. A correspondence has taken place between the Department of State and the Mexican minister of foreign affairs upon the complaint of Mexico that citizens of the United States were permitted to give aid to the inhabitants of Texas in the war existing between her and that Republic. Copies of this correspondence are herewith communicated to Congress, together with copies of letters on the same subject addressed to the diplomatic corps at Mexico by the American minister and the Mexican secretary of state. Mexico has thought proper to reciprocate the mission of the United States to that Government by accrediting to this a minister of the same rank as that of the representative of the United States in Mexico. From the circumstances connected with his mission favorable results are anticipated from it. It is so obviously for the interest of both countries as neighbors and friends that all just causes of mutual dissatisfaction should be removed that it is to be hoped neither will omit or delay the employment of any practicable and honorable means to accomplish that end. The affairs pending between this Government and several others of the States of this hemisphere formerly under the dominion of Spain have again within the past year been materially obstructed by the military revolutions and conflicts in those countries. The ratifications of the treaty between the United States and the Republic of Ecuador of the 13th of June, 1839, have been exchanged, and that instrument has been duly promulgated on the part of this Government. Copies are now communicated to Congress with a view to enable that body to make such changes in the laws applicable to our intercourse with that Republic as may be deemed requisite. Provision has been made by the Government of Chile for the payment of the claim on account of the illegal detention of the brig Warrior at Coquimbo in 1820. This Government has reason to expect that other claims of our citizens against Chile will be hastened to a final and satisfactory close.