The diversion of a hazardous asteroid on a collisional trajectory with the Earth using a transversal thruster is considered. The thruster could be either mounted on the asteroid or used as a “gravitational tractor”. The aim of the study is to establish the fundamental possibility (or impossibility) of diverting an asteroid to a safe distance over a time of order months or years. This is acceptable, since the impact of an asteroid with a diameter of order 100 m on the Earth just after its discovery is very improbable. A model formulation of the problem in which the thruster provides a constant transversal acceleration of the asteroid is used. The corresponding Euler-type equations are transformed using the method of previous averaging. These equations are solved using the method of “slow time” power series, and the adequacy of the solutions over time scales of decades is demonstrated. An asteroid up to 55 m in diameter can be deflected over a year using a 1 N thruster. Asteroids with diameters up to 50 m can be diverted over a month, and with diameters up to 150 m over a year, using a 20 N thruster. Moving larger asteroids requires more time or more powerful engines.