The nation's first test-tube baby clinic today announced it has achieved its second successful pregnancy by implanting a fertilized egg inside the body of a woman who had been incapable of conception.

Officials at the Eastern Virginia Medical School's In Vitro Fertilization Clinic, declined to identify the prospective mother in accordance with the patient's wishes and the program's announced policy of preventing excess strain or liability in the pregnancy because of publicity.

Clinic spokesman Vernon Jones said the first successful impregnation, which was announced in May, "seems to be progressing normally as of this date." Based on information previously supplied by clinic officials, the first pregnancy should be in its 14th week.

If the babies are born, they will be the first conceived through the laboratory process in this country. Babies conceived through in vitro fertilization have been born in England and Australia.

The Norfolk clinic was the first in America to use the in vitro fertilization process. Despite numerous attempts since its opening in March 1980, it took more than a year before a successful pregnancy was announced.

In the in vitro procedure, doctors remove a mature egg from the woman's ovary, fertilize it in a laboratory dish with the husband's sperm and implant the developing embryo in the woman's uterus.

The process is designed for women unable to conceive naturally because of damaged or blocked Fallopian tubes.

Dr. Howard Jones, co-director of the Eastern Virginia Medical School's clinic, credited the successful pregnancies with a "controlled ovulation" process developed at Queen Victoria Hospital in Melbourne.

He said fertility drugs in the form of natural hormones are injected in the patient to control the ovulatory process and allow doctors to implant the fertilized egg at the most opportune time.

A second test-tube clinic in the United States opened last month at the University of Texas in Houston.