The available two-hop relay protocols with out-of-order or strictly in-order reception cannot provide a flexible control for the packet delivery delay, which may significantly limit their applications to the future mobile ad hoc networks (MANETs) with different delay requirements. This paper extends the conventional two-hop relay and proposes a general group-based two-hop relay algorithm with packet redundancy. In such an algorithm with packet redundancy limit $f$ and group size $g$ (2HR-$(f,g)$ for short), each packet is delivered to at most $f$ distinct relay nodes and can be accepted by its destination if it is a fresh packet to the destination and also it is among $g$ packets of the group the destination is currently requesting. The 2HR- $(f,g)$ covers the available two-hop relay protocols as special cases, like the in-order reception ones $(fgeq 1,g=1)$, the out-of-order reception ones with redundancy $(f>1,g=infty)$ , or without redundancy $(f=1,g=infty)$ . A Markov chain-based theoretical framework is further developed to analyze how the mean value and variance of packet delivery delay vary with the parameters $f$ and $g$ , where the important medium contention, interference, and traffic contention issues are carefully incorporated into - he analysis. Extensive simulation and theoretical results are provided to illustrate the performance of the 2HR-$(f,g)$ algorithm and the corresponding theoretical framework, which indicate that the theoretical framework is efficient in delay analysis and the new 2HR-$(f,g)$ algorithm actually enables both the mean value and variance of packet delivery delay to be flexibly controlled in a large region.