What about the kids from a previous marriage

An important factor in each newly created family is the smooth integration of the children from the previous marriage -- definitely when those children are not all the time at daddy's place. Being a dad of two wonderful daughters, I consider any new friend as not OK, if my kids do not feel comfortable with her. This of course becomes extra complicated when more than one friend wants to start living in and with the family. I welcome any suggestions and experiences on this topic, since it is a basic struggle for me to get this question resolved.