This paper presents the results of a bidirectional Hardware-in-the-Loop (HiL) realtime hybrid test on a steel column connected to a two-story reinforced concrete (RC) substructure under earthquake conditions. Two hydraulic dynamic actuators apply the horizontal displacements at the top of the specimen. Nonlinear multi-fiber beam elements model the numerical substructure. The computational cost of the finite element (FEM) analysis is reduced using a Proper Orthogonal Decomposition (POD) Unassembled Discrete Empirical Interpolation Method (UDEIM) with a non-iterative α-Operator Splitting (α-OS) time integration scheme. Data acquisition is carried out using a Linux ® real-time (RT) target, while the dynamic analysis is performed on a Windows ® host computer running custom procedures implemented in MATLAB ® software. A LABVIEW ® interface connects both systems via a lossless stream network. Results on the present case study show that: (1) using a hyper-reduced order model (HROM) can accelerate costly nonlinear dynamic analyses so that they can be run above the sampling period of the ground motion during hybrid tests, and (2) using lossless stream networks calling a MATLAB ® kernel efficiently combines the high data acquisition speed of RT targets (i.e., 10 µs per sample) with the computing power of host computers since the data exchange is quasi-instantaneous.