Wait until you are sure that the relationship is serious and committed. No one can predict how long any relationship will last, but it is important to create stability for the kids. Do not pressure a man to introduce you to his kids until he is confident and ready.
Respect your boyfriend's ground rules. He knows his kids better than you do and is aware of how they might feel. Listen to what he has to say and follow through with his wishes in regard to meeting his kids.
Consider the ages of the kids. Younger kids will not understand a new person in their father's life and attach to other people easily. It is best to wait longer for younger kids than those who are older.
Choose a location that is neutral territory, and preferably public, such as a park, the zoo or a fair. This allows the kids to meet you in a manner that is not threatening to them and incorporates fun for them to relieve some of the pressure of the meeting.
Be patient and take things slowly. Some kids take longer to warm up than others. In this case, some kids are not comfortable with the fact that their father has moved on with someone who is not their mother. Keep the kids' feelings in mind and do not push them to interact with you. Over time, they will become more comfortable with you.
Take your cues from the kids. They will let you know, either verbally or through body language, what they are comfortable with. Watch for these cues and ask your boyfriend to help you interpret them.
Include the kids as often as you can after you have met them. Make them feel like they are important to you. This will make your relationship much better in the long run.