Options in India, except for long-dated contracts, have a maximum of the 3-month trading cycle - 1 month, 2 months and 3 months.
New option contracts are introduced on the next trading day of the expiration of the monthly contracts. The expiration day is the last trading Thursday of the month. So, at any time, buyers have the option to choose from 3 contracts with different expiry dates.
For example, on May 14, 2018, there would be 3 Option contracts i.e. Contracts expiring on May 31, June 28 and July 26. On June 1st, new contracts with the expiry of August 30 would be available for trading.