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As a Christian you can be troubled by evil dreams, voices or other demonic activities. However, there is no reason why you should accept this as 'your lot'. If you have accepted Jesus as Lord of your life then you can be confident of the fact that "the one who is in you is greater than the one who is in the world" (1 John 4:4). The "one who is in you" is Jesus and He is, by far, greater than the devil who is "the one who is in the world". Jesus can shut any 'door' the devil has into your life. Remember Jesus' promise in John 8:36 which says, "if the Son sets you free, you will be free indeed".
When you are saved, you know that your sins are forgiven and that you have eternal life. However, it is still possible for the devil to have access into your life because of issues or activities in your past which you have not fully renounced. If you have been mixed up in occultic practices (things of the devil) or been subjected to occultic activities then that may give the devil the right to part of your life ... the devil then has a doorway into your life and that door has to be shut if you are to be freed from his influences. He won't just go away, the matter must be dealt with. To be delivered from a demonic influence you must confess the occultic connection, renounce it entirely and ask Jesus to set you free.
For example, if you have had contact with palm readers, mediums, ouija boards, magic, witch doctors, shamans, satanism, witchcraft or astrology etc then you need to confess and repent of these things. Go over your life carefully and if even you just think something may be evil then renounce it and ask the Lord to forgive you and deliver you from its influence. Ask Jesus to remind you of all things so that you can deal with all possible occult connections from your past. Also, consider your present life and if there is a sin which you are hanging on to, it must be confessed and renounced.
You should destroy anything you have that may be connected with evil. You may have statues, jewelry, books or something else that is connected with demons. Destroy all these things and if you have a friend who is in the occult then you should pray for them but not associate with them. You must cut yourself off from all that is evil. Don't hold back, get rid of it even if it is valuable. Your salvation is far more important. If you don't get delivered from demonic activity then it may increase and become unbearable and possibly lead you into psychological disorder.
So, go over your life carefully and completely. Renounce every single thing that you think may give the devil a foothold in your life (Eph 4:27). Think carefully and ask the Lord to help you. If you have had anything to do with speaking in tongues, being slain in the spirit etc then repent of all connection with these unscriptural activities. If there are Masons in your family, or if you have had an association with them, then renounce that spiritual tie. Also, renounce any generational/family connections with the occult that you may be aware of. Renounce any connection you may have had with any religion including Buddhism, Hinduism, Mormons, Islam, JWs etc. Above all, ask Jesus to protect you from all evil and to be the Lord of every aspect of your life because all Christians are continually under attack from demons through their thoughts, attacks on family and friends etc. Eph 6:12 tells us that, "our struggle is not against flesh and blood, but against the rulers, against the authorities, against the powers of this dark world and against the spiritual forces of evil in the heavenly realms."
If you are half-hearted about any of this then it is not likely that you will be delivered. Just like sin, demons will stick around until you finally mean business and want them out of your life.
There is a list of occultic/demonic connections on page 28 of the book 'The Christian, His Enemies And His Armour' which is free to download from: http://www.christianissues.biz/thechristian.html
This book will be very helpful to anyone suffering from demonic activity and p.33 outlines steps to take in resisting demons.
For several free books showing the error of modern day tongues, please go to: http://www.christianissues.biz/tongues.html
On page 17 of the book Today's Tongues there is a 'Declaration Of Victory' prayer to renounce demonic activities.