The present paper introduces two bonds in a standard New-Keynesian model to study the role of segmentation in bond markets for the determinacy of rational expectations equilibria. We use a strongly-separable utility function to model 'liquid' bonds that provide transaction services for the purchase of consumption goods. 'Illiquid' bonds, instead, provide the standard services of store of value. We interpret liquid bonds as mimicking short-term instruments, and illiquid bonds to represent long-dated instruments. In this simple setting, the expectation hypothesis holds after log-linearizing the model and after pricing the bonds according to an affine scheme. We assume that monetary policy follows a standard Taylor rule. In this context, the inflation targeting parameter should be higher than one for determinacy of rational expectations equilibria to be achieved. We compute an analytical solution for the bond pricing kernel. We also show that the possibility of obtaining this analytical solution depends on the type of utility function. When utility is weakly separable between consumption and liquid bonds, the Taylor principle holds conditional to the output and inflation coefficients in the Taylor rule. Achieving solution determinacy requires constraining these coefficients within bounds that depend on the structural parameters of the model, like the intertemporal elasticity of consumption substitution.