We theoretically study the spin dynamics in antiferromagnets (AFs) under the influence of an electric current. We identify two different sources of spin-transfer torques that stem from uniform (v n ) and staggered (v ) electron spin densities. While the former is well recognized, the latter is often overlooked. We show that both v n and v contribute equally to the spin-wave Doppler shift. Microscopic calculations are presented for electrons on a two-dimensional square lattice with nearest-neighbor (t) and next-nearest-neighbor (t ) hopping, which interpolate two opposite transport regimes of strongly-coupled AF (t /t 1) and two weakly-coupled ferromagnets (t /t 1). In the AF transport regime (t /t 1), v n and v have opposite signs, and the sign of the Doppler shift depends on band filling; v n (v ) is dominant near the AF gap (near the band bottom or the top). As t /t is increased, v n undergoes a sign change whereas v does not. In the limit of vanishing t, v n and v coincide and the spin-transfer torque reduces to that of ferromagnets.