The main objective of this thesis is to provide solutions to some combinatorial testing issues. The combinatorial testing consists in generating tests that cover all combinations of defined input values. The first issue of this thesis is that combinatorial testing can generate a large number of tests that are invalid according to the specification of the System Under Test (SUT). These invalid tests are typically those which fail the verification of the precondition of system operation. These invalid tests must be discarded from the set of tests used to evaluate the SUT, because they lead to inconclusive verdicts. As a solution, we propose to couple the combinatorial testing technique to an animation technique that relies on a specification to filter out invalid tests. In our work, combinatorial tests are generated from a test pattern. This pattern is mainly defined as a sequence of operation calls, using a set of values for their parameters. The unfolding of a complex test pattern, where many operation calls and/or input values are used, may be subject to combinatorial explosion, and it is impossible to provide valid tests from the test pattern. This is a second issue of this thesis. As a solution, we propose an incremental unfolding and animation process that allows to filter out at early stage (in the operation sequence) invalid tests, and therefore to master the combinatorial explosion. Other mechanisms of filtering are proposed to filter out tests which do not cover some operation behaviors or do not fulfill a given property. The test suites generated from a test pattern can be very large to execute on the SUT due the limited memory or CPU resources. This problem is defined as the test suite reduction problem, and it is the third issue of this thesis. As a solution, we propose a new test suite reduction technique based on annotations (called tags) inserted in the source code or the specification of the SUT. The execution/animation of tests generates a trace of the covered annotations. Based on the trace, a family of equivalence relations is proposed, to reduce a test suite, using the criteria of order and number of repetition of covered tags.