Guide to Marriage Nullity Procedures

Formal Nullity 
The judicial process that may result in a declaration of marriage nullity is a “formal process” or what some refer to as an “annulment.” 

Privilege of the Faith case (Petrine Privilege) 
This may apply if a party to a marriage was not baptised, and one of those parties now wishes to marry a baptised Catholic.

Also known as favour of the faith, it is a ground recognised in Catholic canon law that allows the Pope to grant dissolution of a valid natural marriage between a baptised and a non-baptised person, for the sake of the salvation of the soul of someone who is thus enabled to marry in the Church.

Defect of Canonical Form 
This procedure applies where a Catholic married in a non-Catholic religious ceremony or in a civil ceremony, and with no dispensation from a Catholic bishop. 

Your local parish priest should be able to help you with this.

Pauline Privilege case 
This procedure may apply where both partners were unbaptised.  A party seeking baptism can invoke this privilege by which their Christian sacramental marriage dissolves the natural bond of their first marriage.