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HD 18955 is a double-lined spectroscopic binary with a period of 43.3214 days and a high eccentricity of 0.761. The spectral types of the components are K0 V and K2-K3 V. The secondary is a typical early K dwarf, although its minimum mass is greater than canonical values. However, this larger mass is consistent with other early K dwarf, spectroscopic binary results. The primary is anomalous, being substantially underluminous for its radius and mass, which are equal to or slightly greater than solar values. A lack of lithium argues that the components are not pre-main-sequence stars. The large minimum masses of both components suggest that the system has a high orbital inclination. Our photometric observations around the times of conjunction show no evidence of eclipses, but considering the uncertainties in the ephemerides, there is only a 50% chance that our photometric observations would have detected the primary eclipse and almost no chance that we covered the secondary eclipse. Hence, eclipses remain a real possibility in this system. Photometric variations with an amplitude of 0.02 mag reveal a period of 7.55 days, which is assumed to be the primary star's rotation period. Thus, given the spectral types of the stars, this system is a BY Draconis type variable. With vsini values of 5 km s-1 for both components, the two stars are rotating more rapidly than typical K dwarf field stars, but the observed rotation period is still substantially longer than the predicted pseudosynchronous rotation period of 4.6 days for the primary.