For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
          Tony Flores
        Many people and even Satan and demons believe in Jesus Christ, but that does not mean that they have accepted Him as Lord and Savior of their lives. Jesus Christ is the Way, the Truth and the Life and only through Him can you have eternal life. God sent His Son to die for our sins, which He did at the Cross, if you believe in Him by Faith and have a personal relationship with Him and follow him, you will be saved, because by just believing that He existed at a time in History will still take your path to the Lake of Fire.
          Singapore Moses
        Who can be saved?
✿ One of the reasons why people dispute over the possibility of present assurance of salvation is that they fail to understand salvation in three tenses. Salvation past is deliverance from the "penalty" of sin; salvation present is deliverance from the "power" of sin; and salvation future is deliverance from the very "presence" of sin. Respectively they are called Justification, Sanctification and Glorification. The first one is a crisis experience, the next one is a process, and the last one is a crisis again, which will take place at a moment. We are already saved from the penalty of sin. We are being saved, moment by moment, from the power of sin. But removal of the presence of sin is still in the future.
✿ Our assurance may be shaken up as we walk through trials, tribulations and temptations. During the turbulence of this present time, the "Spirit Himself bears witness with our spirit that we are the children of God" and He assures us that "the sufferings of the present are not worthy to be compared with the glory which shall be revealed in us" (Rom 8:16,18).
✿ Our sins which were red like crimson have been made whiter than snow by Jesus. He bore them all on the Cross of Calvary. As far as the East is from the West, so far He has removed our sins from us. He has cast them behind His back. He has thrown them into the depths of the sea. They disappeared like the clouds of the sky. Oh, the breadth, the length, the depth and the height of God's forgiving love! We need not doubt our salvation a bit!
          Danny Hickman
        Tony Flores, you said something very informative; it's also a little cloudy. Yes, Satan and his demons know who Jesus is. And no, they don't (as you put it) "accept" Jesus as Savior.
Let's examine that. What if a demon did "accept" (not my idea, others believe in the idea of accepting Him) Jesus? What if a demon thought it over and decided, "I think I'd rather live with God in Paradise than die," and changed their mind about "accepting" that Jesus can save him?
Does anyone see the flaw in that? God CHOOSES to bring us whom HE SAVES to repentance. It isn't left up to us to change our mind, or think it over and come to the right decision, or anything like that. If so, what would prevent demons from doing it? We know from Scripture that they know who Jesus is. 
They are evil! They can't "make a decision" that leads to salvation, and neither can we! Yes, they know that Jesus is the Son of the living God and all the rest. Knowing that isn't how we are saved. We must be born of the Spirit of God. The Spirit is like the wind. He blows wherever He chooses (John 3).