The evolution of unmagnetized beam‐driven strong Langmuir turbulence is studied in two dimensions by numerically integrating the Zakharov equations for systems pumped by monochromatic and broadband negative‐damping drivers with nonzero central wavenumber. Long‐time statistically steady states are reached for which the dependence of the evolution on the driver wavenumber, growth rate, and bandwidth is examined in detail. For monochromatic drivers, a quasiperiodic cycle is found to develop if the driver wavenumber is sufficiently large. In this cycle, energy from the driven mode undergoes a sequence of weak‐turbulence backscatter decays, which transfer energy to an approximately isotropic long‐wavelength condensate. During this phase, beam‐aligned chains of propagating beat waves develop and perpendicular density waves are also excited. Subsequently, nucleation of waves in density cavities causes a series of wave collapses (involving coherent wave–wave interactions) to occur, during which short‐wavelength damping reduces the system energy in discrete steps. Finally, the cycle restarts. The characteristic frequency of the quasiperiodic cycle and the average system energy are both approximately proportional to the growth rate. Broadening of the driver in wavenumber tends to degrade the system‐wide coherence of the cycle, but its main features appear to survive on the scale of the coherence length of the driver.