The manifestation of the structural and magnetic properties of Co substituted TiFe2 is investigated using powder X-ray diffraction, magnetization and density functional theory calculations. The alloys TiFe2 and TiFeCo crystallize in the hexagonal structure (P63/mmc) with a reduction in the lattice parameters of TiFeCo (by about 0.51% in a and 0.64% in c) when compared to TiFe2. On the other hand, TiCo2 crystallizes in the cubic structure (Fd3[combining macron]m). A structural transition from hexagonal to cubic is anticipated for a composition with x ∈ [0.5, 1]. The non-collinear antiferromagnetic (AFM) spin structure (formed by 6h Fe atoms) of TiFe2 with Néel temperature TN ∼ 275 K is reported at zero magnetic field H. Meanwhile, a magnetic field-induced collinear antiferromagnetic spin structure is suggested by magnetization measurements and supported by density functional theory calculations. The magnetization of TiFeCo shows a weak-ferromagnetic (FM)-like transition around 204 K, followed by a broad hump at 85.5 K and H = 200 Oe. Ferromagnetic interactions are weakened, causing the hump to disappear due to the possible transfer of electrons between Fe and Co. TiCo2 shows compensated ferrimagnetism with magnetization of the order of 10-5μB f.u.-1 and a linear increase of M with H at 5 K. The presence of a non-collinear AFM spin structure in TiFe2, a reduced magnetic moment in TiFeCo due to the charge transfer between Co and Fe, and compensated ferrimagnetism in TiCo2 promise a rich phase diagram of Ti(Fe1-xCox)2 alloys and the possible potential of these alloys for use in spintronics applications.