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The recently recognized class of "transitional disk" systems consists of young stars with optically thick outer disks but inner disks which are mostly devoid of small dust grains. Here we introduce a further class of "pre-transitional disks" with significant near-infrared excesses which indicate the presence of an optically thick inner disk separated from an optically thick outer disk; thus, the spectral energy distributions of pre-transitional disks suggest the incipient development of disk gaps rather than inner holes. In UX Tau A, our analysis of the Spitzer IRS spectrum finds that the near-infrared excess is produced by an inner optically thick disk and that a gap of similar to 56 AU is present. The Spitzer IRS spectrum of LkCa 15 is suggestive of a gap of similar to 46 AU, confirming previous millimeter imaging. In addition, UX Tau A contains crystalline silicates in its disk at radii [unk] 56 AU which poses a challenge to our understanding of the production of this crystalline material. In contrast, LkCa 15's silicates are amorphous and pristine. UX Tau A and LkCa 15 increase our knowledge of the diversity of dust clearing in low-mass star formation.