Transactional Memory (TM) is a speculative shared-memory synchronization mechanism used to speed up concurrent programs. Most current TM implementations are software-based (STM) and incur noticeable overheads for each transactional memory access. Hardware TM proposals (HTM) address this issue but typically suffer from other restrictions such as limits on the number of data locations that can be accessed in a transaction. In this paper, we introduce new hybrid TM algorithms that can execute HTM and STM transactions concurrently and can thus provide good performance over a large spectrum of workloads. The algorithms belong to the class of time-based TM designs and exploit the ability of some HTMs to have both transactional and non-transactional memory accesses within a transaction to decrease the transactions' runtime overhead, abort rates, and hardware capacity requirements.