We examine the suppression of 1+1 photodissociation or photoionization by laser fields. We find that atoms and molecules become more stable against photoionization or photodissociation when the intensity of the nonresonant laser field is increased above a limiting value for a two level plus continuum model system. We treat the ionization or dissociation dynamics analytically and discuss the conditions for optimum yields in a two-frequency square pulse laser field. We observe similar suppression against photodissociation for realistic sine-squared laser pulses. We demonstrate such a type of molecular suppression for 1+1 photodissociation of H-2. (C) 2003 American Institute of Physics.