The traditional analysis of sound reflection and transmission at an interface between two lossless fluids is for plane waves and a plane interface. Considered here is reflection and transmission of a spherical wave at a concentric spherical interface, either concave or convex. The pressure reflection (R) and transmission (T) coefficients are found to be complex; the coefficients for a convex interface are complex conjugates of those for a concave interface. Among the (somewhat surprising) results are these. First, although at high frequency the expressions for R and T are the same as for plane waves, at low frequency R→−1 regardless of the value of the ratio ρ2c2/ρ1c1, (provided ρ2≠ρ1). Second, perfect transmission requires both ρ2=ρ1, and c2=c1, not just ρ2c2=ρ1c1. Third, if the source is a monopole and the interface radius a→0, the sound power transmitted into the second medium is that expected for a single fluid; the same is not true, however, if the source is a dipole. [Work supported by ONR, NASA, and Southampton University.]