» Sayyiduna Abu Ayyub (Radi Allahu Anhu) has narrated the following statement of the Holy Prophet (SallAllahu Alayhi wa Sallam):

‘‘Whoever keeps fasts in Ramadan and then keeps six fasts in Shawwal, it is as if he has kept fasts for his entire life.’’ [Sahih Muslim, Page 592, Hadith 1164]

 
» Sayyiduna Sauban (Radi Allahu Anhu) has narrated that the Prophet of mankind, the Peace of our heart and mind, the most Generous and Kind (SallAllahu Alayhi wa Sallam) has said:

‘‘The one fasting six days after Eid-ul-Fitr (in Shawwal) has fasted the entire year because whoever brings one good deed will get ten rewards (for it).’’ [Sunan Ibn Majah, Vol. 2, Page 333, Hadith 1715]

 
» Sayyiduna Abdullah bin Umar (Radi Allahu Anhu) has narrated that the Noble Prophet (SallAllahu Alayhi wa Sallam) has said:

‘‘The one fasting in Ramadan and then fasting six days in Shawwal has been cleansed from sins as if he was born from his mother’s womb today.’’ [Majma’ al-Zawaid, Vol. 3, Page 425, Hadith 5102]

 
NOTE: It is better to have these six fasts separately (on alternate days or after every two/three days), but there is still no harm if somebody fasts consecutively after Eid-ul-Fitr. [Bahar-e-Shari’at, Part 5, Page 140]