The second pillar is: Presence of the two spouses who are free of impediments that cause marriage to be invalid such as: a woman should not be prohibited for a man to marry because of lineage, suckling, `Iddah (woman's prescribed waiting period after divorce or widowhood), a man should not be a disbeliever while a woman is a Muslim among other impediments. 
Women who are prohibited to marry according to Shari`ah are of two types:
· The first type is:
Permanent unmarriageable women (in all times and all cases) who were mentioned in Allah's Saying: “Forbidden to you (for marriage) are: your mothers, your daughters, your sisters, your father's sisters, your mother's sisters, your brother's daughters, your sister's daughters, your foster mothers who gave you suck, your foster milk suckling sisters, your wives' mothers, your step-daughters under your guardianship, born of your wives to whom you have gone in, but there is no sin on you if you have not gone in them (to marry their daughters), the wives of your sons who (spring) from your own loins, and two sisters in wedlock at the same time, except for what has already passed; verily, Allâh is Oft-Forgiving, Most Merciful." 
Those permanent unmarriageable women are of three types:
• First, unmarriageable women by kinship: including the mother, grandmothers, and grand grandmothers. Daughters, granddaughters, and grand-granddaughters whether they are lawfully begotten or not.
Full sisters and half-sisters (paternal or maternal).
Nieces and grand nieces.
Daughters of brother's sons.
Paternal or maternal aunts.
The proof to those is Allah's Saying: “Forbidden to you (for marriage) are: your mothers, your daughters, your sisters, your father's sisters, your mother's sisters, your brother's daughters, your sister's daughters.”
• Second, unmarriageable women by suckling who have the same ruling as women who are unmarriageable by kinship ”Your foster mothers who gave you suck, your foster milk suckling sisters.” because of the Prophet's saying: “Suckling renders women unmarriageable as birth renders women marriageable." 
• Third, unmarriageable women by marriage relationship (affinity) and they are of two types: A type that is prohibited once the marriage contract is signed even before sexual intercourse and they are: The step mother even by suckling and the wife of grandfathers and grand grandfathers because of Allah's Saying: “And marry not women whom your fathers married.”  The son's wife and the son's son's wife even if they are by suckling because of Allah's Saying: “And the wives of your sons.” The wife's mother and grandmother are also prohibited to be married because of Allah's Saying: “Your wives' mothers.”
The second type is women who are prohibited by marriage once the sexual intercourse between a husband and wife takes place which are: The wife's daughters and daughters of her children downwards either by kinship or suckling because of Allah's Saying: “Your step-daughters under your guardianship, born of your wives to whom you have gone in.”
· The second type is:
Temporary unmarriageable women who are as follows:
First, women who are prohibited because of combination like a woman and her sister because of Allah's Saying: “And two sisters in wedlock at the same time.” And a woman and her paternal or maternal aunt because of the Prophet's saying: “A woman and her paternal aunt should not be married to the same man; and similarly, a woman and her maternal aunt should not be married to the same man.”  Likewise, it is prohibited to marry a fifth woman until a husband divorces one of his four wives and the divorcee’s `Iddah is terminated because he is not allowed to marry more than four because of Allah's Saying: “Then marry (other) women of your choice, two or three, or four.” 
Second, women who are prohibited for a reason which are the women who are still in their waiting period until their `Iddah is terminated because of Allah's Saying: “And do not consummate the marriage until the term prescribed is fulfilled.”  Wives who were divorced three times should not be married to their husband until they marry another man willingly then are divorced for any reason and their `Iddah is terminated because of Allah's Saying: “And if he has divorced her (the third time), then she is not lawful to him thereafter until she has married another husband. Then, if the other husband divorces her, it is no sin on both of them that they reunite, provided they feel that they can keep the limits ordained by Allâh. These are the limits of Allâh, which He makes plain for the people who have knowledge.”  Women who are in the state of Ihram (ritual state for Hajj and `Umrah) because of the Prophet's saying: “A Muhrim (one who is in the state of Ihram for Hajj and `Umrah) must neither marry himself, nor arrange the marriage of another one, nor should he make the proposal of marriage.”  Adulteress until she repent because of Allah's Saying: “The adulterer-fornicator marries not but an adulteress-fornicatress or a Mushrikah, and the adulteress-fornicatress none marries her except an adulterer-fornicator or a Muskrik [and that means that the man who agrees to marry (have a sexual relation with) a Mushrikah (female polytheist, pagan or idolatress) or a prostitute, then surely he is either an adulterer-fornicator, or a Mushrik (polytheist, pagan or idolater). And the woman who agrees to marry (have a sexual relation with) a Mushrik (polytheist, pagan or idolater) or an adulterer-fornicator, then she is either a prostitute or a Mushrikah (female polytheist, pagan, or idolatress)]. Such a thing is forbidden to the believers (of Islâmic Monotheism).”  The disbelieving woman, unlike the People of the Scriptures, until she embraces Islam because of Allah's Saying: “And do not marry Al-Mushrikât (idolatresses, etc.) till they believe (worship Allâh Alone).”  And Allah's Saying: “Likewise hold not the disbelieving women as wives.”  As for the chaste women of the Scriptures, it is permissible for a Muslim to marry because of Allah's Saying: “And chaste women from those who were given the Scripture (Jews and Christians) before your time.”  .
1- See Hashiyat Ar-Rawd Al Murbi` 246\6 that only mentioned the most frequent pillars and did not mention this pillar because it is quite obvious, however some scholars mentioned these conditions.
2- [Surat An-Nisa': 23].
3- [Reported by Al Bukhari, book of marriage, chapter on “And your foster mothers who gave you suck.” page 5099-140 \9 in Fathul-Bary and also reported by Muslim, book of suckling 18\10 in the commentary of An-Nawawy].
4- [Surat An-Nisa': 23].
5- [Reported by Al Bukhari, book of marriage, chapter on "a woman and her aunt are not married to the same man at the same time, p. 5109-160\9 in Fathul-Bary, and was also reported by Muslim, book of marriage, chapter on "the prohibition of combining between a woman and her paternal and maternal aunt in marriage, p. 33-134\4].
6- [Surat An-Nisa': 3].
7- [Surat Al Baqarah: 235].
8- [Surat Al Baqarah: 230].
9- [Reported by Muslim, book of marriage, chapter on "the prohibition that a Muhrim marries during the state of Ihram and the reprehensibility of making a proposal of marriage" 194\9 in the commentary of An-Nawawy].
10- [Surat An-Nur: 3].
11- [Surat Al Baqarah: 221].
12- [Surat Al Mumtahinah: 10].
13- [Surat Al Ma'idah: 6].
14- [See: Sharh Ar-Rawd Al Murbi` 294\6-312 and Manar As-Sabil 161\2-171].