If the product of an addition reaction is unstable under the reaction conditions and undergoes a substitution reaction, the overall reaction is called an addition-substitution.

eg:

mechanism:

The first stage of the mechanism, shown in black, is an acid-catalyzed addition.  The addition product, hemiketal 1, is unstable under acidic conditions and undergoes a nucleophilic substitution, shown in blue, via activation of the hydroxy group by the acid.  Thus, the overall reaction is an addition-substitution.

See also addition-elimination.

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