Marriage/'Nikah' according to Muslim Law is a contract underlying a permanent relationship based on mutual consent.
REQUIREMENTS
The solomonisation of marriage requires adherence to certain forms and formulas. They are called the essentials of a valid marriage. If any of these requirements is not fulfilled the marriage becomes either void or irregular, as the case may be. Thus the essentials are as follows:
1. Proposal and Acceptance
2. Competent parties
3. No legal Disability
According to Muslim Law it is absolutely necessary that a man or someone on his behalf and the woman or someone on her behalf should agree to the marriage at one meeting and the agreement should be witnessed by two adult witnesses.The Words conveying proposal and acceptance must be uttered in each other's presence or in the presence of their agents, who are called Vakil's.The other condition for a valid marriage is that the transaction must be completed at one meeting. A proposal made at one meeting and an acceptance at another meeting do not constitute a valid marriage.There must be reciprocity between offer and acceptance. The acceptance must not be conditional.The parties contracting marriage must be acting under their free will and consent.It is essential amongst the Sunnis that at least two male witnesses or one male or two female witnesses must be present to testify that the contract was properly entered into between the parties. The witnesses must be of sound mind, adult and Muslim.
In Shia Law, a marriage contracted by the spouses themselves or their guardians in private are held valid. Presence of witnesses is not necessary.More over a marriage of a Muslim female with a non-Muslim male, whether he be a Christian, or a Jew or an idolator or a Fire-Worshiper is irregular under Sunni Law and void under Shia Law.
The law and the religion both do not permit a Muslim man to perform another marriage as of a right by defeating and delaying the rights of his first wife.Muslim men are preached that they can marry for the second time only if they are able to be equitable to both the women. "In the same breath the surah nisa further states that practically this is not possible and therefore second marriage should not be contracted because it will cause injustice
So mere affidavit does not leads to a valid marriage. A Muslim man married according to Shariat Muslim Law can have four Muslim wives legally on certain conditions. So their marriage is not a valid one.