GETTING THERE: There are no direct flights from the United States to either Eilat or Aqaba. El Al Airlines flies from Washington to Tel Aviv, where you can connect with an El Al or Arkia flight to Eilat. The current APEX fare from Washington, including the flight to Eilat, is $1,164 round trip; the ticket must be purchased two weeks in advance.

Or, once in Tel Aviv, you can take a bus to Eilat for about $10. The trip takes from five to six hours.

To get from Eilat to Aqaba, you must travel from the Taba checkpoint (about 15 minutes from central Eilat via bus or taxi) into Egypt, to Nuweiba. There is public transportation from Taba to Nuweiba -- the bus fare is about $5 -- or you can take a taxi for about $20 (less if you share). From Nuweiba, a ferry will take you to Aqaba for $35 one way, second-class -- although, because these boats are primarily for workers and pilgrims, tourists are frequently upgraded to first-class at no additional charge. The trip takes from three to four hours.

Another option, of course, is to reverse the whole procedure and start out in Jordan. From Washington, you can fly to Amman and connect there with a flight to Aqaba. Royal Jordanian Airlines' current APEX fare from Washington to Aqaba is $966 round trip; the ticket must be purchased two weeks in advance. Another option is to fly to Amman and take a bus from Amman to Aqaba for about $5. From Aqaba, catch the ferry to Nuweiba and proceed through Taba to Eilat.

VISAS: Visas are required of American citizens entering Jordan and Egypt. Applications may be obtained from the Jordanian Embassy, 3504 International Dr. NW, Washington, D.c. 20008, 966-2664, and the Egyptian Consulate, 2300 Decatur Pl. NW, Washington, D.C. 20008, 234-3903.

When applying for a Jordanian visa, be prepared to confront an application question concerning religion. The current policy permits entry to Jews; it also allows persons to leave the question unanswered. However, a visa will not be granted if a passport bears the stamp of Israel. Then if you wish to visit Jordan as well as Israel, it is mandatory that you request upon entry to Israel that your passport not be stamped. (Israeli authorities will readily oblige.)

In addition, since there have been reports of persons being turned back by Jordanian officials because the "Taba" stamp in their passports indicated they had been in Israel, it is wise to request that the Egyptian border officials not stamp passports (which they may or may not agree to do).

A visa is not required for American citizens entering Israel. However, there have been reports of Arab-Americans and black Americans being harassed by Israeli immigration officers, and the U.S. Department of State has warned Israel that it may issue a travel advisory.

INFORMATION: For information on Eilat Israeli Tourist Office, 364-5546 in Washington, (212) 560-0650 in New York. There is a tourism office in Eilat, located in the Rechter Center directly across from the central bus station, phone (059) 722-68.

In addition, independent tour operators in the area (in Eilat, Neot Hakikar or Muki Meltzer, in Nuweiba, Centa Misr) can be invaluable in helping to arrange trips.

For information on Aqabe: Jordan Information Center, 1701 K St. NW, Washington, D.c. 20006, 659-3322.