This paper introduces SPECULA, a novel replication protocol for Software Transactional Memory (STM) systems that seeks maximum overlap between transaction execution and replica synchronization phases via speculative processing techniques. By removing the replica synchronization phase from the critical path of execution of transactions, SPECULA allows threads to speculatively pipeline the execution of both transactional and/or non-transactional code. The core of SPECULA is a multi-version concurrency control algorithm that supports speculative transaction processing while ensuring the strong consistency criteria that are desirable in non-sand-boxed environments like STMs. Via an experimental study, based on a fully-fledged prototype and on both synthetic and standard STM benchmarks, we demonstrate that SPECULA can achieve speedups of up to one order of magnitude with respect to state-of-the-art non-speculative replication techniques.