When I have a Master which to need to communicate with many slaves through the RXD,TXD pins, is it possible for the slaves to communicate with master independently. That is whenever the slave wants to do so. The reason why I asked is if there is an attempt by more than one slave to communicate with the Master at the same time, won't it cause a conflict? If so, how such situations to be handled?
Yes - that would be your "protocol".
IF the slaves listen while they transmit, and you have a suitable design of the "start byte", you can use this for collision detection...