Yes you can have a baby after 35 but there are certain factors and potential risks to keep in mind. The fertility of men and women changes with age. Research shows that a woman's peak fertility occurs between the ages of 19 - 26. It also shows that as a woman ages beyond 35 (and especially after age 40), the likelihood of getting pregnant drops very quickly. The age of men seems to be an influencing factor only beyond 35 years1. If you are trying to have a baby past the age of 35, do not get discouraged if it takes a little longer. Keep trying. If you are unsuccessful at becoming pregnant even after 6 months of regular sex, go see a doctor.
Research also shows that incidence of Down Syndrome and other birth defects in babies increases after 35 years of age. The likelihood that a woman under 30 who becomes pregnant will have a baby with Down syndrome is less than 1 in 1,000, but the chance of having a baby with Down Syndrome increases to 1 in 400 for women who become pregnant at age 35. The likelihood of Down Syndrome continues to increase as a woman ages, so that by age 42, the chance is 1 in 60 that a pregnant woman will have a baby with Down Syndrome, and by age 49, the chance is 1 in 12. Many specialists recommend that women who become pregnant at age 35 or older undergo prenatal testing for Down Syndrome2 to mitigate the risk.
But age is not the only factor responsible for birth defects. There could be others including exposure to harmful chemicals, genetic history, smoking, and dietary shortcomings.
This also does not mean that you should have a baby early or not have a baby after 35, but you need to be aware of the risks and get the appropriate tests done at the right times. These tests include AFP (Alpha-Feto Protein), and Amniocentesis.
1. Dunson, David B., Baird, Donna D., Colombo, Bernardo "Increased Infertility With Age in Men and Women", Obstet Gynecol 2004 103: 51-56
2. Hook, EG, Lindsjo A. "Down syndrome in live births by single year maternal age interval in a Swedish study: comparison with results from a New York State study." Am J Hum Genet. 1978 Jan;30(1):19-27