Summary: For a Lebesgue integrable complex-valued function \(f\) defined over the \(n\)-dimensional torus \(\mathbb {I}^n:=[0,1)^n\) \((n\in \mathbb N)\), let \(\hat f({\mathbf k})\) denote the multiple Walsh-Fourier coefficient of \(f\), where \({\mathbf k}=(k_1,\dots,k_n)\in (\mathbb {Z}^+)^n\), \(\mathbb {Z^+}=\mathbb {N}\cup \{0\}\). The Riemann-Lebesgue lemma shows that \(\hat f({\mathbf k})=o(1)\) as \(|{\mathbf k}|\to 0\) for any \(f\in L^1(\mathbb I^n)\). However, it is known that, these Fourier coefficients can tend to zero as slowly as we wish. When \(n=1\) the definitive results are due to the author and J. R. Patadia [JIPAM, J. Inequal. Pure Appl. Math. 9, No. 2, Paper No. 44, 7 p. (2008; Zbl 1160.42012)] for functions of certain classes of functions of generalized bounded variation. The author [Acta Math. Hung. 128, No. 4, 328–343 (2010; Zbl 1240.42025)] defined the notion of bounded \(p\)-variation (\(p\geq 1\)) for a function from a rectangle \([a_1,b_1]\times\dots \times [a_n,b_n]\) to \(\mathbb {C}\) and obtained definitive results for the order of magnitude of multiple trigonometric Fourier coefficients. In this paper, such definitive results for the order of magnitude of multiple Walsh-Fourier coefficients for a function of bounded \(p\)-variation are obtained.