First, be sure he's actually divorced or at least legally separated. There are those who will say they "are getting divorced" but are still living in the same house and maybe even sleeping in the same bed with their ex-to-be. The marriage may be over emotionally but not really over so there's a long bumpy road ahead for him.
It's important to clarify exactly where he is along the spectrum and end it quickly if he is not out of the marital home. Despite what he believes and says, he is not ready. If you choose to go ahead, you are choosing that bumpy long road for yourself as well.
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Second, understand there are various, predictable emotional stages of separation and divorce. The longer the marriage, the longer the adjustment takes. The experience is even more intense when there are children involved.
Shock, disbelief, refusal to accept, anger, grief, begging for another chance, perhaps marital counseling or psychotherapy for one or both partners, finally giving up and the legal process — a disorienting time in itself — are all part of the emotional, financial, practical and parental adaptation.
Even after the legal process has been concluded, there is still processing and evaluation to be done by a newly divorced person. It takes at least a couple of years from the initial separation to go through the loss and pain and actually become truly open and available to another partner.
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You will see a lot of emotional vacillation as he finds his way through the morass. You will need to be excessively patient and have few demands of your own.
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