I left my husband almost two years ago. He refused to sign seperation agreement and we still have no property settlement nor a divorce. I have one minor child that resides with me full-time and maybe stays with his dad once a week. My ex-spouse is now stating that he wants to pursue alimony. My question is how will a judge look at this if the ex-spouse has lived two years without alimony would he even have a case?

Much more than the amount of time that has passed is taken into consideration by the court when determining an alimony award, but the delay would certainly work against him if he pursues a claim.