Two Northwest Washington men, one 18 and the other 19, were arrested yesterday and charged in the fatal shooting of Young Ja Cha, a 42-year-old Korean immigrant who was killed during an exchange of shots with robbers who held up the grocery store she ran on an inner-city street corner.

Police said the arrests of the two men, who live within three blocks of the victim's store, followed interviews with witnesses and residents.

Cha, who with her husband had owned the Sherman Market at the corner of Sherman Avenue and Columbia Road NW for about four years, was a well-liked figure in the row house neighborhood around the store, whose customers praised her friendliness and generosity.

Police said Theodore R. Rhem, 18, of 1307 Columbia Rd. NW, was arrested at his home about 7 a.m. They said Darion Jerome Willis, 19, of 1305 Columbia Rd. NW, was arrested about the same time at the home of a friend several blocks away.

Both were arrested on warrants charging them with felony murder.

Police said that at about 2:30 p.m. Friday, three men entered the store and an attempt was made to rob Cha. A small amount of money was taken; according to some detectives the sum was less than $50. During the robbery, police said, Cha was shot in the abdomen. Police said Cha returned the gunfire. The robbers fled, and Cha, fatally wounded, emerged from the store and collapsed, bleeding, into a cardboard carton on the sidewalk.

At a hearing yesterday in D.C. Superior Court, Assistant U.S. Attorney Neil Hurley said Rhem had acknowledged being in the store around the time of the robbery. Rhem's court-appointed defense lawyer, Enid Hinkes, said her client was not involved in the crime and had left the store before it occurred.

Commissioner Tom Gaye ordered Rhem held without bond pending an appearance in a police lineup on March 19 and a preliminary hearing March 21.

The presentment for the second suspect was postponed until today. Police Capt. Larry Soulsby, head of the homicide unit, said at a news conference at noon that Willis was being taken to D.C. General Hospital for treatment of a wound to the right hand that police believed was caused by a bullet.

Police said they were looking for a possible third.

In an apparent response to reports in the past of possible friction between Korean owners of inner-city stores and their largely black clientele, police said, they will hold a meeting tomorrow to air any differences that may exist.

The meeting is to be held at 7 p.m. at the 4th Police District headquarters at 6001 Georgia Ave. NW, according to Inspector Richard J. Pennington, police community relations chief. Soulsby indicated doubt that such intergroup conflict was involved in the Cha shooting, noting Cha's popularity in the community.