Let \(\phi\) be an Orlicz function (convex function \(\phi : {\mathbb R}_+ \to {\mathbb R}_+\) such that \(\phi (0)= 0\), \(\phi (u) >0\) for \(u > 0\), \(\phi(u)/u \mathop{\longrightarrow} 0\) for \(u \to 0\) and \(\phi(u)/u \mathop{\longrightarrow} \infty\) for \(u \to \infty\)). The Besicovitch--Orlicz space \(B^\phi ({\mathbb R})\) is the space of measurable functions \(f\) on \({\mathbb R}\) such that \(\rho_{B^\phi} (\lambda f) 0\), where \(\rho_{B^\phi} (f) = \overline{\lim}_{T \to\infty} {1 \over 2T} \int_{-T}^T \phi (| f(t)| )\,dt\), endowed with the Luxemburg norm \(\| f\| _{B^\phi} = \inf\{ k>0 \mid \rho_{B^\phi} (f/k) \leq 1\}\) (it is actually a semi-norm; one considers the associated normed space). The Besicovitch--Orlicz space of almost periodic functions \(B^\phi\)-a.p.\ is the closure in \(B^\phi ({\mathbb R})\) of the set of the trigonometric polynomials \(\sum_j \alpha_j \exp(i \lambda_j t)\). In [\textit{M.\,Morsli}, Ann.\ Soc.\ Math.\ Pol.\ (I) Commentat.\ Math.\ 34, 137--152 (1994; Zbl 0839.46012); see also Funct.\ Approximatio, Comment.\ Math.\ 22, 95--106 (1993; Zbl 0831.46019)], the first author studied the uniform convexity of \(B^\phi\)-a.p.\ with the Luxemburg norm. In the paper under review, the present authors do the same with the Orlicz norm (defined by duality: \(||| f||| _{B^\phi} = \sup\{ M(| fg| )\); \(g\in B^\phi\)-a.p., \(\rho_{B^\psi} (g) \leq 1\}\)), where \(\psi\) is the conjugate of the Orlicz function \(\phi\) and \(M(f)=\lim_{T\to \infty} {1 \over 2T} \int_{-T}^T f(t)\,dt\). They prove that \(B^\phi\)-a.p.\ is uniformly convex with the Orlicz norm if and only if \(\phi\) satisfies the usual \(\Delta_2\) condition and is uniformly convex, meaning that for every \(a \in ]0,1[\), there exists a \(\delta (a) \in ]0,1[\) such that \(\phi \big({u + au \over 2}\big) \leq \big(1 - \delta (a)\big) {\phi (u) + \phi (au) \over 2}\) for \(u\) large enough. In order to prove the necessity, they show that there is a natural isometry from \(E^\phi ([0,1])\) into \(B^\phi\)-a.p.\ (for both the Luxemburg and Orlicz norms), where \(E^\phi ([0,1]) =\{f\mid\int_0^1 \phi\big(\lambda | f(t)| \big)\,dt 0\}\) is the Morse--Transue space.