| Although the Standard Model(SM) has achieved much success in the field of particle physics, it introduces Higgs scalar field to explain the mechanism of the breaking of electroweak symmetry. It is the elementary scalar field that generates a series of questions, for example, it creates the questions of triviality and unnaturalness, etc. Thus, the SM can only be an effective field theory below some high energy scale. There may be new physics beyond the SM. Little Higgs theory is one of the important promising candidates of new physics. The littlest Higgs(LH) model has been constructed based on the ideas of the little Higgs theory, which predicts the existence of new heavy gauge bosons Zh, Bh and W(H|+). These particles might produce characteristic signatures at the present and future collider experiments. In this paper, we study the signatures of these new particles in the future high-energy linear e+e-colliders(ILC).At first, we consider the contributions of these new particles to the Higgs boson production associated with top quark pair in the future ILC. We find that, for reasonable values of the free parameters, the absolute value of the relative correction parameter δσ/σSM can be significanly large, which might be observed in the future ILC experiment with S1/2 = 800GeV. Second, we calculate the contributions of these new particles to the processes e+e-→f|-f with f = τ,μb, or c and study the possibility of detecting these new particles via these processes in the future ILC experiments with s1/2 = 500GeV and £int = 340fb-1. We find that, with reasonable values of the free parameter, the possible signals of these new particles might be detected. The Zh mass MzH can be explored up to 2.8TeV via the process e+e-→b|-b for 0.3 ≤c ≤0.5 and the Bh mass Mbh can be explored up to 1.26TeV via the process e+e-→l|-l for 0.64 ≤c≤0.73. Third, we consider the processes e+e-→vv|-H0 and e+e-→W*W*vv|-→vv|-tt|-, and calculate the contributions of new particles to the cross sections of these processes in the future ILC with S1/2 = 1TeV. We find that the deviations of the cross sections for the processes e+e-→vv|-H0 from its SM value might be comparable to the future ILC measurement precision. The contributions of the new gauge bosons Bh and Zh to the process e+e-→W*W*vv|-→vv|-tt|-are very small, which can not be detected in the future ILC experiments. Finally, we study single production of the new gauge bosons Bh, Zh and W(H|+) via e-γcollisions and discuss the possibility of detecting these new particles in the TeV energy ILC. We find that these new particles can not be detected via the evv signal in all of the parameter space. However, the heavy gauge bosons Bh and Zh may be observed via the decay channel Bh(Zh) →l+l-in wide range of the parameter space.In a word, it is possible to detect the signatures of these new particles in the future ILC experiments. |