Reaching consensus on the global state of a ledger among distributed participants is an important challenge in blockchain systems. There are many consensus approaches studied to required that trust should be reduced or eliminated. The most commonly used consensus approaches in blockchain systems, for example, Proof ofWork (PoW) approach consumes large amounts of power, but transaction throughput is limited. Consensus approaches such as Proof of Stake (PoS) is proposed to mitigate this outstanding issue. However, these consensus methods have concentration of wealth of participants, allowing wealthy‚ÄövÑvp stake holders to have high probability controlling block's generation. That conducts a small subset of nodes have power to control creation of blocks in blockchain network. Furthermore, most existing consensus methods failed to maintain a proper balance between security and performance in the ledgers. This thesis analyses some of the most commonly used consensus approaches in blockchain systems. The thesis presents detail on consensus approaches for reaching the agreement. Based on this analysis, two novel blockchain consensus approaches are proposed. Proof of SecureStake (PoSS) is proposed to address imbalance of wealth and the security of the ledgers over block generation, and Proof of Assurance (PoAssu) is proposed to enhance performance in transaction throughput for per second.