This study investigates, using a new variable-acceleration model, the validity of the implicit assertion in previous studies regarding global constant sea level rise accelerations. Thirteen out of twenty seven globally distributed tide gauge stations, with records longer than 80 years, exhibit statistically significant quartic coefficients (p < 0.05) revealing the presence of variable sea level accelerations though not as a global phenomenon. Most of these stations initially exhibit decreasing negative velocities until early 20th century and increasing positive velocities after 1970’s following a period of constant velocities. It is shown that, for those locations experiencing statistically significant variable sea level accelerations, the estimates based on the conventional linear representation of linear sea level trends are not appropriate, and are notably biased for a number of stations. All solutions account for serial correlations, which otherwise induce biases in solution statistics. It is also demonstrated that the omission of non-linearities in sea level changes will bias the sea level trends for short records, such as those from satellite altimetry, as large as 3 mm/yr.