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The millimeter/submillimeter spectrum of magnesium chloride (MgCl) has been observed in two new electronic excited states, (3)2Σ+ and (4)2Σ+, using direct absorption methods. The molecule was synthesized in a mixture of Cl2, argon and magnesium vapor. For the (3)2Σ+ state, multiple rotational transitions were measured in the v = 0 level for all six isotopologues (24Mg35Cl, 24Mg37Cl, 25Mg35Cl, 25Mg37Cl, 26Mg35Cl, 26Mg37Cl), as well as up to v = 13 for 24Mg35Cl. For the (4)2Σ+ state, less intense spectra were recorded for 24Mg35Cl (v = 0-2). Equilibrium rotational parameters were determined for both states for 24Mg35Cl, as well as rotational constants and 25Mg hyperfine parameters for the other isotopologues. A perturbation was observed between rotational levels of the two states due to an avoided crossing. Computations were also carried out at the CASPT2 and MRCISD+Q levels, and the resulting bond lengths for (3)2Σ+ and (4)2Σ+ states agree well with the experimental values of re = 2.536 Å and 2.361 Å. The computations show that the (3)2Σ+ state has a double-well potential; however, the state behaves as a single well with unperturbed vibrational levels up to v = 13 due to non-adiabatic coupling with the (4)2Σ+ state.