  This article extends the theory of classical finite-difference
summation-by-parts (FD-SBP) time-marching methods to the generalized
summation-by-parts (GSBP) framework. Dual-consistent GSBP time-marching methods
are shown to retain: A and L-stability, as well as superconvergence of integral
functionals when integrated with the quadrature associated with the
discretization. This also implies that the solution approximated at the end of
each time step is superconvergent. In addition GSBP time-marching methods
constructed with a diagonal norm are BN-stable. This article also formalizes
the connection between FD-SBP/GSBP time-marching methods and implicit
Runge-Kutta methods. Through this connection, the minimum accuracy of the
solution approximated at the end of a time step is extended for nonlinear
problems. It is also exploited to derive conditions under which nonlinearly
stable GSBP time-marching methods can be constructed. The GSBP approach to time
marching can simplify the construction of high-order fully-implicit Runge-Kutta
methods with a particular set of properties favourable for stiff initial value
problems, such as L-stability. It can facilitate the analysis of fully discrete
approximations to PDEs and is amenable to to multi-dimensional spcae-time
discretizations, in which case the explicit connection to Runge-Kutta methods
is often lost. A few examples of known and novel Runge-Kutta methods associated
with GSBP operators are presented. The novel methods, all of which are L-stable
and BN-stable, include a four-stage seventh-order fully-implicit method, a
three-stage third-order diagonally-implicit method, and a fourth-order
four-stage diagonally-implicit method. The relative efficiency of the schemes
is investigated and compared with a few popular non-GSBP Runge-Kutta methods.
